Midras Mazmur 51:6: Ein Yaakov (Glick Edition), Sifrei Devarim & Midrash Tehillim

(Deut. 32, 4) The God of truth, and without iniquity. God of truth, i.e., just as the wicked will be punished in the world hereafter even for the slightest offense which they may commit here on earth, so also are the righteous to be held to account in this world even for the slightest transgression committed; And without iniquity; i.e., just as the righteous will be rewarded in the future world even for the least meritorious act, so also are the wicked rewarded in this world even for the least meritorious act. (Ib.) Just and right in He. They [Our Rabbis] say that when a man dies and comes into the world beyond, all his deeds are laid open before him in detail, and he is told: "So and so hast thou done in that place and on that day." Whereupon he answers: "Yea," and he is told to sign his name, which he signs, as it is said (Job 37, 7) He sealeth it on the hand of every man. And not this alone, but he also acknowledges the justice of the verdict and says: "You have judged me righteously," to justify the passage (Ps. 51, 6) In order that thou mayest he righteous when thou speakest, be justified when thou judgest.

Raba lectured: "What does the passage (Ps. 11, 1) In the Lord have I put my trust; how can ye say to my soul, flee to your mountain as a bird mean? i.e., David said before the Holy One, praised be He! 'Sovereign of the Universe! forgive me this sin so that people shall not say that your mounatin was lost through a bird'." (Fol. 107) Raba lectured: "What is the meaning of the following passage (Ps. 51, 6) Against Thee, Thee only, have I sinned, and done that which is evil in Thy eyes; in order that Thou mayest be justified when Thou speakest, and be in the right when Thou judgest, i.e., David said before the Holy One, praised be He! 'Sovereign of the Universe, it is known and revealed before Thee, that if I had desired to curb my passion, I would have succeeded, but I did not, so that people should not say that the servant conquered his master'." Raba lectured again: "What is the meaning of the passage (Ib. 38, 18) For I am ready to halt, and my pain is continually before me. Bath Sheba was destined for David since the six days of creation; however, she came to him only through infliction." And so also it was taught at the college of R. Ishmael: Bath Sheba, the daughter of Eliam, was destined for David, but he enjoyed her as an unripe fruit. Raba lectured: "What is the meaning of the passage (Ps. 35, 15) But when I halt they rejoice, and gather themselves together; … they tear me, and cease not. Thus said David before the Holy One, praised be He! "Sovereign of the Universe, it is known and revealed before Thee that if they would tear my flesh the blood would not run. Even when they are occupied in the study of Negaim and Ahaloth they say to me: 'David, who is an adulterer, with what kind of a death must he be punished?' And I answered them: 'He is to be hanged; he, however, has a share in the world to come, but he who exposes his fellowmen to shame in public has no share in the world to come'."

And when Nathan the Prophet came and rebuked David for that act, he said (Ibid. 13) "I have sinned to the L-rd," and (Psalms 51:3) "Be gracious (chaneini) to me, O G-d, according to Your lovingkindness … (6) To You alone have I sinned and what is evil in Your eyes have I done."