What is the meaning of "Kis'acha Elokim Olam va'Ed"?
Rashi: Your throne is an officer and judge forever. Elohim is like "Nesaticha Elohim l'Pharaoh" (Shemos 7:1).
Radak citing Rav Sadya Gaon: Elokim will establish your throne.
Radak citing Ibn Ezra: Your throne is Elokim's throne. Malbim - this is because you sit on it in order to judge Emes and Tzedek, like Elokim. Since it is [like] the Divine, it will last forever. 1
Radak: Notzerim say that this Mizmor applies to their savior. He is called Melech and Elokim. They err 2 .
Malbim (Derech ha'Muskal): The intellect sits on Kisei Elokim to rule absolutely over the Nefesh. It is Kisei Elokim, for it comes from a Divine Ru'ach from above.
Radak citing Ibn Ezra: This is like "va'Yeshev Shlomo Al Kisei Hashem" (Divrei ha'Yamim I, 29:23).
Radak: It says "Shemen Sason me'Chaverecha" (verse 8) - Elokim does not have colleagues! It says "Shegal li'Minecha" (verse 10). One cannot say, even as a metaphor, that Hashem lies with a woman! It says "Tachas Avosecha Yihyu Vanecha" (verse 16). Indeed, we are Hashem's Banim (Devarim 14:1), but He does not have fathers!
Why does it say "Shevet Mishor Shevet Malchusecha"?
Rashi: This is why "Kis'acha Elokim Olam va'Ed" - because your judgment is Emes, and you are proper to reign.
Malbim: This is a metaphor, as if straightness is a living being that conducts the kingdom with its staff. This is the staff of your kingdom, i.e. your straight conduct.
Malbim (Derech ha'Muskal): Straightness fixed in his heart, in mindsets, Emunah and action, to do what is good and straight in the eyes of Elokim and man, is the staff with which he conducts kingship over the powers of the Nefesh.