Not a bad question if you live in the first century. Most Christians today will tell you without hesitating that the answer to that question is Jesus. What's interesting is the diversity of meaning once held by a title that today has so singular a meaning. Even though in the Old Testament no individual ever addresses God as "Father", the reality is that the term existed before the incarnation (and was sometimes used of 'incarnate' pagan gods). The question is, if we were to ask a Jew in the first century BC who the son of God was, what would s/he tell you?

Adam

The easiest answer to comprehend or accept for us 21st century Christians is probably the idea that Adam was understood to be the son of God. Consider Luke 3:38, the end of Jesus' genealogy. Having listed off the various sons of sons through David, Abraham and Noah we come to the last father: Adam. Except Adam is not the last Father. Because we read that Adam is in fact, "the son of God". The surprise here is not that Adam is the Son of God, but that Jesus is and that Jesus is a son like no other (see Luke 3:22)!

Angels

In Job 1:6 we read that "the day came when the sons of God presented themselves before YHWH and the Adversary was with them" and as we continue reading we realise that we are watching a scene unfold in the throneroom of heaven and these sons of God must be angels with Satan/the Adversary, the angelic being, among them. The NET Notes on this verse are illuminating,

They are not actually "sons" of Elohim; the idiom is a poetic way of describing their nature and relationship to God. The phrase indicates their supernatural nature, and their submission to God as the sovereign Lord. It may be classified as a genitive that expresses how individuals belong to a certain class or type, i.e., the supernatural (GKC 418 §128.v). In the pagan literature, especially of Ugarit, "the sons of God" refers to the lesser gods or deities of the pantheon.

In his Study Bible, John Macarthur claims that sons of God are "identified elsewhere almost exclusively as angels" and cites the three occurrences from Job. This is, however, an overstatement. Job is the only clear biblical presentation of this usage. Nevertheless, to an ancient Israelite "sons of God" could be an angelic reference.

Israel

Perhaps one of the surprising answers to the question posed is that the nation of Israel is understood to be the son of God. In Exodus 4:22 YHWH is telling Moses how the plagues will play out and it culminates in the instruction to tell Pharaoh, "Israel is my son, my firstborn" and on that basis, Israel should be freed to worship. The final plague, the death of the firstborn is, therefore, justified on the basis of aspect of Israel's identity "since you have refused to let him [my son] go, I will surely kill your son, your firstborn!" (Exodus 4:23).

Likewise Jeremiah 31 expresses the same understanding of Israel's identity. The images are mixed among the picture of Israel as a virgin but in 31:9 we read,

I will bring them back praying prayers of repentance.
I will lead them besides streams of water,
along smooth paths where they will never stumble.
I will do this because I am Israel's father;
Ephraim is my firstborn son.

So in addition to Adam and angelic beings, Israel is also on occasion referred to as God's son.

Kings

As we read the Old Testament we discover one further somewhat unexpected referent of "son of God". While the Psalms are littered with this sort of reference the most evocative reference is surely 2 Samuel 7 in which YHWH promises David in verse 12,

When the time comes for you to die, I will raise up your descendant, one of your own sons, to succeed you, and I will establish his kingdom.

But most significantly verse 14,

I will become his father and he will become my son.

So the King of Israel, God's king for God's people could also be referred to as the son of God.

Caesar

Finally, one important factor that we would be remiss to overlook is the fact that first century Israel was under Roman occupation. This meant that the idea of who the son of God was did not stem only from Jewish tradition but also from the Graeco-Roman context. NT Wright puts it beautifully in his Simply Jesus saying that Octavian, having won the power struggle,

He declared that his adoptive father, Julius, had indeed become divine; this meant that he, Augustus Octavian Caesar, was now officially 'son of god', 'son of the divine Julius'.

Wright continues, describing a coin on his desk engraved with a depiction of Tiberius,

On the front, encircling Tiberius's portrait, is the abbreviated title: AUGUSTUS TI CAESAE DIVI AUG F, short for, AUGUSTUS TIBERIUS CAESAR DIVI AUGUSTI FILIUS, "Augustus Tiberius Caesar, son of the Divine Augustus". On the reverse is a picture of Tiberius dressed as a priest, with the title Pontifex Maximus. It was a coin like this one that they showed to Jesus of Nazareth, a day or two after he had ridden into Jerusalem, when they asked him whether or not they should pay tribute to Caesar.

In other words in the first century, one important answer to the question, "who is the son of god?" was certainly, "Caesar".

Nephilim & the sons of God (Genesis 6)

Now when we reach Genesis 6 and we read in verse 2 that, "the sons of God saw that the daughters of humankind were beautiful. Thus they took wives for themselves from any they chose," we need to figure out who the sons of God are. Especially since the passage continues with one of the most enigmatic biblical references, "The Nephilim were on the earth in those days ... when the sons of God were having sexual relations with the daughters of humankind, who gave birth to their children." So the question "who were the Nephilim" is entwined with the question of who the sons of God were.

MacArthur explains Nephilim by the etymological root of the term as "fallen ones" and therefore also explains sons of God as fallen angels (he cites Jude 6 and 2 Peter 2:4,5 - neither of which are clearly about this passage let alone use parallel terms). It is doesn't make much sense to think of angelic beings and humans reproducing.

Another popular explanation is that the sons of God are the 'godly' line of Seth - as opposed to the godless line of Cain. Of course, this use of the term is entirely unattested. Diving into such a view also suffers the theological belly flop of producing sinless people after the fall.

To interpret the sons of God as kings, however, parallels its later usage and makes pretty good sense of the text. We find that the mighty men, men of renown, are their descendants. What we often forget is that the primary measure of leadership today has nothing to do with physical strength because today brain normally beats brawn. In the ancient world, however, this would not have been the case. So if the sons of God were kings they would have probably been tough guys, probably bearing the genetic material to produce "men of renown". The one thing left unsolved by this explanation is the reason for the term "Nephilim" but since the meaning "fallen ones" is basically a guess, I don't think it's a major loss to say we've lost the significance of the term.

So there you have it, the simplest and neatest (and most Ockham's Razorly) explanation of the sons of God in Genesis 6 is that sons of God refers to kings and the Nephilim are their big children. There is, however, something far more exciting that we find by tracing the uses of sons of God.

The Son of God in Biblical Theology

While there is diversity to the term "son of God", within the diversity there is something quite spectacular going on with this elusive character. You see ultimately Christians have forgotten all these other usages in favour of one much later usage: Jesus.

The cool thing about Jesus being the son of God is that he is the second Adam. That's important because in Adam all die and in Christ all are made alive. So Jesus needs to be the son of God like that.

Another cool thing is that Jesus being the son of God lines up pretty neatly with his representative headship over the people of God. Calling Israel the son of God is kind of like calling Jesus the son of God because the significance of the designation is in the special calling and relationship with God.

Similarly, calling a king the "son of God" had to do with the king's position of headship over God's people. In the case of Jesus, Jesus as the true king of Israel is again in this sense the "son of God".

Jesus completes each of these meanings by bringing them to fulfilment in himself. He is the true Adam who never sins, the true Israel who never rebels and the true king of God's kingdom who leads rightly. Jesus walks righteously with God and earns his headship and our righteousness, qualifying him as the son of God. But he is more than any of these shadows because Jesus is, in all his fullness, ultimately God the Son.