Why did David compose this Mizmor?
Rashi (2): It is primarily about the Beis ha'Mikdash, even though Chachamim expounded it about Moshe and Aharon (refer to 133:1:2:1).
Malbim: It is about two known brothers - Yisachar and Zevulun. They joined together like a body and Nefesh, that one goes on a path to perfect the other. "Semach Zevulun b'Tzeisecha v'Yisachar b'Ohalecha" (Devarim 33:18). Yisachar engaged in Torah to perfect the Nefesh, and Zevulun engaged in commerce to perfect the body and acquisitions. Via joining together, "Tov" and "Na'im" were completed - the true good in matters of the world to come, and pleasantness of temporary life.
What do we learn from "Sheves Achim Gam Yachad"?
Horiyos 12a: Moshe was concerned lest he transgressed Me'ilah (by putting two drops more than needed on Aharon - Rashi Kerisus 5b). A voice from Heaven proclaimed "like the good oil (that descends on Aharon's beard)...; like the dew of Chermon" - just like there is no Me'ilah in the dew of Chermon, also in the Shemen ha'Mishchah in Aharon's beard. Aharon was concerned lest he transgressed Me'ilah (perhaps the oil went where it was not needed, and he benefited from it.) A voice from Heaven proclaimed "... Achim Gam Yachad" -just like Moshe did not transgress, also Aharon.
Rashi: This refers to when Hashem will dwell in the Beis ha'Mikdash with Yisrael, who are called Achim and Re'im; also He will be together with them.
Radak citing his father: This refers to Yisrael; they are all brothers. Their dwelling in Yerushalayim was good and pleasant, like "good oil that descends on Aharon's beard and garments" (2), or like "dew of Chermon that descends on it and on mountains of Tziyon" (3). It is more blessed than all dew that descends in the world.
Radak citing Ibn Ezra: This refers to Kohanim mentioned above (132:16). "Achim" refers to the company of Kohanim. "Gam" refers to the Kohen Gadol; it mentions Aharon (verse 3), for he was the first anointed Kohen Gadol.
Radak: It refers to Melech ha'Mashi'ach and the Kohen Gadol 1 who will be in his days. They are the greatest in Yisrael, and masters over them. The king sits on the throne of Mishpat and the kingship to command Yisrael to do as he sees and wants. The Kohen teaches Torah and Mitzvos. They are called Achim, for they have grandeur and do not envy one another. Just like they are brothers in grandeur, also in their hearts they will agree.
Malbim: Refer to 133:1:1:1.
Radak: Similarly, when they ascended from Galus Bavel, Zecharyah prophesized about both of them - Zerubavel the Nasi and Yehoshua the Kohen Gadol. He saw them as two olives - "Shnei Bnei ha'Yitzhar" (Zecharyah 4:14), for both were anointed with Shemen ha'Mishchah - "v'Asisa Ataros v'Samta b'Rosh Yehoshua; ...Hinei Ish Tzemach Shmo" (ibid., 6:11-12). The latter refers to Zerubavel. Also about them it says "va'Atzas Shalom Tihyeh Bein Sheneihem" (ibid., 13).
