Which United States presidents had documented mistresses/habitually cheated on their wives?

The evidence we have strongly supports the theory that Thomas Jefferson had a long-running sexual relationship with one of his slaves (who was also the half-sister of his wife).

Nine months before each of her children's birthdates, Jefferson is documented to be near her. Jefferson gave all of her surviving children freedom. In addition to the rumors, genetic testing on one of her descendants shows a genetic link to Jefferson. (Incidentally, this happened before Bill Clinton and the famous dress, which meant Clinton's infidelity was the second one to be proven via DNA testing, not the first).

Now there are alternative explanations with Jefferson not being the father, but they appear far less convincing (I believe most try to place the blame on another male Jefferson relative). The DNA test I'm referring to was a Y-DNA test (Y-chromosome, passed from father-to-son without change), so it's possible there's another explanation, but the other explanations aren't as plausible.

For other presidents, Grover Cleveland recognized an illegitimate child before he was president. Interestingly, there's some question if he was the father (he may have been covering for married friends). If anyone else can chime in on this case, I'd be curious. I know the various theories, but I'm not sure which one is the consensus.

Warren G. Harding had a famous affair before his presidency but while he was a married man. This is documented by letters to his mistress, which she kept.