What do I do to prove I love my boyfriend?

You have to ask yourself if you really do love him. Because for the rest of your relationship you are going to have that cloud hanging over you and he will have it in his back pocket every time you fight. It will suck. I have seen relationships try to work after someone admits to cheating. Sometimes its about the severity of the cheating but if its bad you will never truly live it down. unless he cheats. You know you screwed up and I am just going to make the assumption that it was under the "best" circumstances, not that there are any. To prove that you love him. you will have to sacrifice something or a lot of little things. For starters you are going to be sacrificing to stay in the relationship. He will have a lot of control for a long time. The easy thing to do would be to just give up and not have to deal with it.

Sorry, but I have to agree with Random. You screwed up. To be honest, it is better just to move on and find another guy, because you screwed the pooch on this relationship. Trust is 100% or it's nothing. And chances are, he won't ever trust you completely.

You have to earn his trust and respect back. Apparently, you didn't love him enough as you cheated on him and broke his heart.

go on a break with him, earn his trust back and don't cheat again

if you loved him, you wouldn't have cheated. but everyone gets scared, in a relationship, or they get sick of it and feel a need to move on. but if you're really devoted and willing to earn his love (in meaning it too) talk to him about it. because, every relationship deserves a second chance, if you're willing to take it.

If you really love him, you will know the answer.

if you have to ask then I don't think you really love him. but if you feel really bad and want to get as much of his trust back as you can, just try and do things with him that he likes to do, but don't put your needs on the back burner