I believe with the person you are responding to. Admitting you were going slightly over the speed limit won't really hurt you.

They don't need a confession to cite you for speeding. They already know if you were or not.

I've probably been pulled over 8 times in my life and only gotten two tickets. Who knows - this could have to do with my race or my demeanor - but in general I just try to act as honestly and apologetically as possible. I think most police officers are not trying to be jackasses, and the ones that are will ticket you whether or not you "fess up" or not anyway.

(This probably doesn't hold if you are carrying drugs or going 25mph over, but otherwise I don't think it helps to treat these interactions so adversarially)

The only times I've been asked "Do you know why I pulled you over?" was when I had a tail light out. I figured the reason they asked was to see if I was already aware of the problem. In one case, I was literally on my way to buy a new headlight, and they accepted that as an answer and sent me on my way.

You're directionally correct - it's important not to admit to something that the officer doesn't already know - but your example is not a good one, since the cop is going to know you're speeding in this case. You certainly shouldn't admit to having a bunch of drugs, though.