ὁ Θεὸς in Heb 1:8 can either be construed as a subject nominative, nominative of address or a predicate nominative.
Interestingly, William Tyndale evidently understood ὁ Θεὸς as a subject nominative.
"But unto the son he saith: God thy seat shall be for ever and ever" (Tyndale's NT).
C.F.D. Moule writes: "Luke XVIII.11 ὁ Θεὸς (Heb. 1:8, which looks similar, may conceivably be a true Nominative, construed so as to mean Thy throne is God; but see commentators IN LOC.) . . ." (An Idiom Book of NT Greek, p. 32).
As is known by those familiar with issues related to the Trinity doctrine and Christology, B.F. Westcott also favored the translation "God is your throne."
In his commentary on Hebrews, he writes: "The phrase'God is Thy throne' is not indeed found elsewhere, but it is in no way more strange than Ps LXXI.3 [Lord] be Thou to me a rock of habitation . . . Thou art my rock and my fortress" (p. 26).
It is also obvious that the term "throne" applied to God in Heb 1:8 is not to be taken literally; God is understood as the one who upholds, guarantees or supports the Messiah's kingly rule.
Furthermore, in this case, God is not said to be a throne for His people. He is, according to Westcott and Tyndale, the Son's Throne. While M.J. Harris does not favor this interpretation of Heb 1:8, he nevertheless says that the expression "God is your throne" must mean "your throne is founded on (or protected by) God" since it is a metonomy not belonging to the category of the divine (see Jesus As God, p. 213).
What is so hard to understand about God being Jesus' throne in that He upholds or supports his kingship? After all, the ancient Davidic kings of Judah also had God as their throne since they sat upon the figurative throne of YHWH (1 Chron 28:5; 29:23). To me, a similar idea is being communicated in Heb 1:8.