Rashi, from Sanhedrin 70b: Bas Sheva tied Shlomo to a beam and lashed him (for eating too much). "Mah Bri..." - why did you do this, and inform that you are my son, and not your father's son? All know that your father is a total Tzadik - if you are a Rasha, they will say that his mother caused this! "U'Mah Bar Bitni" - David would not have Bi'ah with his other wives when they were pregnant. I asserted myself, for this improves the fetus. "U'Meh Bar Nedarai" - David's other wives (prayed and) vowed what they would do if they would have a son proper for kingship. I vowed in order that my son should be zealous, a Chacham, and proper for prophecy.

Rashi: It is words of Shlomo, that he said to Hashem, i.e. because he was crooked to Hashem. L'Mu'el is like la'Kel, like "l'Mo Fi" (Iyov 40:4. It is as if it says l'Fi; the Men and Vov are extra - Ibn Ezra there) - matters that the king said to Hashem's name. When Shlomo married Bas Pharaoh, on the day of Chanukas Beis ha'Mikdash ¹ , she brought in many instruments. He was awake the entire night, and slept the next day until four hours, like it says in Pesikta. The keys of the Mikdash were under his head. It was taught about that time that the Tamid can be offered at four hours. His mother entered and rebuked him for this act.

Malbim: It is a Sefer of Musar that his mother rebuked him, to Lemu'el, king of Masa.