Need Relationship Advice. Last chance?

My boyfriend and I were dating for 3 years. But just before our 3rd anniversary, we broke up. The reason being he was cheating. I gave him a lot of chances to fix his cheating. But he continued with the same girl. And ultimately knocked her up. I broke up with him. He always flirted and cheated behind my back. I don't doubt his love. Yes he loved me truly but was disloyal and took advantage of me and took me for granted. Now it's been 6 days of break up and he's begging me to come back just so he could prove he has realized his mistakes. He regrets treating me that way and wants to prove that he wants to fix everything. He wants to be the man I imagined him to be. He truly wants me back and is trying all he can. He says he doesn't want to make false promises but wants to prove by his actions that he really wants me and no one else. He realizes his mistake he says. He only wants to prove and is not asking me back. Should I let him prove? Should I give him that one last chance?