In order to comprehend the point in a better perspective a reading of Mtt 22: 41-46 would help:
Now while the Pharisees were gathered together, Jesus asked them this question: “What do you think of the Messiah? Whose son is he?” They said to him, “The son of David.” He said to them, “How is it then that David by the Spirit calls him Lord, saying,
‘The Lord said to my Lord,
“Sit at my right hand,
until I put your enemies under your feet”’?
If David thus calls him Lord, how can he be his son?” No one was able to give him an answer, nor from that day did anyone dare to ask him any more questions
Now, Hebrew 1:8 (NRSVCE) goes :
"But of the Son he says,
“Your throne, O God, is forever and ever,
and the righteous scepter is the scepter of your kingdom.
Mind that Hebrew 1:8 is in fact, an excerpt from Psalms 45:4-6:
In your majesty ride forth victoriously
in the cause of truth, humility and justice;
let your right hand achieve awesome deeds.
Let your sharp arrows pierce the hearts of the king’s enemies;
let the nations fall beneath your feet.
Your throne, O God, will last for ever and ever;
a scepter of justice will be the scepter of your kingdom.
The writer of Hebrews has borrowed the words of David and attributed them to God the Father. Hence the confusion.