Dovid was born in Sin

  Tehilim (051:07):. Behold, I was shaped in iniquity, and in sin my mother conceived me.

Alshich (Tehilim 51:7): Behold in sin I was formed – From the time it decreed that I should be born by means of the sin of Lot’s daughter who had an incestual relation with her father which is disgusting and terrible sin – but that is how I was formed. As it says in Bereishis Rabbah (50:16), “I found Dovid My servant” where was he found? In Sedom. And in sin my mother conceived me - that is referring to Ruth who is referred to as mother as it says in Bava Basra (91b)... she was the mother of the Davidic monarchy. From the time when she got the idea of lying at the feet of Boaz which was the sin of chilul Hashem as we see in Ruth Rabbah (6:1) that Boaz prayed that no one would know that she came to the threshing floor. And You G‑d did not consider it bad since You knew the motivation was good....

 Kotzker Rebbe (Emes v’Emuna p635):The biblical prohibition on adultery included relations with one’s own wife if they involved sexual desire.

Rashi (Tehilim 51:7): Behold I was formed in transgression – So how could I not sin. The basis of my being formed was my parents sexual intercourse and through intercourse it is possible to be involved in a number of transgression. And alternative explanation, my principle formation was from male and female – both of them are full of sins. However there are other interpretive readings to this verse and they do not conform to the subject matter of the verse.

 Vayikra Rabbah (14:05) In sin I was formed … Dovid said before G-d, did my father actually have intent to have me or was he was he focused on his own pleasure? Obviously it was for pleasure because when they finished, my father and mother both turned their faces away from each other.