But of the Son he says, “Your throne, O God, is forever and ever, the sceptre of uprightness is the sceptre of your kingdom. You have loved righteousness and hated wickedness; therefore God, your God, has anointed you with the oil of gladness beyond your companions.” (Hebrews 1:8)
There are two possible readings of ‘God’ in verse eight. Either in the vocative (‘your throne, O God …’) or as the subject (‘God is your throne …’). So this verse may not be addressing Jesus as God at all. It is also worth remembering that Hebrews 1:8-9 is quoting a psalm (Psalm 45), which was first applied to a human king.
2 You are the most handsome of the sons of men;
grace is poured upon your lips;
therefore God has blessed you forever.
3 Gird your sword on your thigh, O mighty one,
in your splendor and majesty!
4 In your majesty ride out victoriously
for the cause of truth and meekness and righteousness;
let your right hand teach you awesome deeds!
5 Your arrows are sharp
in the heart of the king’s enemies;
the peoples fall under you.
6 Your throne, O God, is forever and ever.
The scepter of your kingdom is a scepter of uprightness;
7 you have loved righteousness and hated wickedness.
Therefore God, your God, has anointed you
with the oil of gladness beyond your companions;
8 your robes are all fragrant with myrrh and aloes and cassia.
From ivory palaces stringed instruments make you glad;
9 daughters of kings are among your ladies of honor;
at your right hand stands the queen in gold of Ophir.
Some read that if the psalmist thought it appropriate to call a man ‘god’ then would it not also be appropriate for Jesus to be called ‘god’ in this context. The problem with that is that the Old Testament clearly teaches that there is “no Elohim but One” (Isaiah 45:5). Also, in no place in the New Testament is Jesus called God. There are a small number of verses where that is claimed but in each case the claim is surprisingly weak.
It is also worth bearing in mind that the terms ‘therefore’ and ‘anointed’ in this passage imply subordination. The psalmist is saying that the king, and later Jesus, “love righteous and hated wickedness” and it was for this reason (hence “therefore”) that God gave him a new status. If Jesus was God he would be de jure entitled to the throne and sceptre by his very nature. The psalmist is saying that these things were given to Jesus by God.
For a related question: Is the king of Israel called “god” in Psalm 45:7 – “Your throne, O God,”?
And for a list of 10 verses on this topic: Does the Bible call Jesus ‘God’? (10 verses which some say do)