What did Hashem say with His mouth?
Rashi: He will give to him a son who will build the Bayis (Shmuel II, 7:14).
What is the meaning of "uv'Yado Milei"?
Rashi: He fulfilled His word with His good hand.
Radak: With His power and ability; He caused all nations to make Shalom with Shlomo, and do his will.
Radak citing Targum Yonasan: With His desire, He fulfilled.
Malbim: Hashem's word immediately takes effect; it is as if the matter was done, for everything is via His word and decree. However, this is not for matters that depend on people's choice. Then it is not fulfilled until He veers a person to do like Hashem said. Shlomo could have refrained from building the Bayis; fulfilled with His hand, and bent the king's heart until he fulfilled Hashem's word.
Why does it say "Leimor"?
Radak: This refers back to "Hashem
