Should I give my cheating boyfriend a second chance?

[Confused Girl]

Me and my boyfriend just celebrated our 6th anniversary last January. We have a 4 year-old daughter. Days ago, I just caught him cheating big time. This is the story:

Last June 2013, we had a fight because he caught me keeping in touch with my first boyfriend. We broke up. But it didn't last and in less than a month we made up. He confessed that during that time when we were apart, he hooked up with some girl but he told me that he already broke up with her the time we fixed our relationship. I never suspected him since I am not that kind of woman. For 8 months we been like that, me trying to please him to make up for my mistakes and him making all those demands and always suspecting about me that I am doing something wrong again. But just few days ago, I don't know what pushed me but I stalked the facebook profile of that girl he told me he was hooking up with and my instincts didn't fail me. I saw a status which said " <3 See you soon _____ (name of my boyfriend)" and the date was february 14. I was so shocked since this never happened to us before (me catching him cheating). I didn't see it coming. I confronted the girl first to confirm and she told me everything. They've been together for 8 months and she claimed that she didn't know we were together again. Had she known, she would've stayed away from us. Now to make the long story short I broke up with my boyfriend. And now he's asking for a second chance.
He said that he loves us so much (me and our daughter) and that what he did was a big mistake and that he'd change and that he never loved the girl and so on and so forth.

Should I believe him that he'd not do it again and give him a second chance or should I just end everything? Please help, I'm so confused right now.
Another question: when a man says he'll never cheat again, would there be a chance that he'd really mean it? Like, do men change really, or is a cheater always a cheater? Thanks, I really appreciate all your comments/advices.