How can I get him to admit that he cheated?

Okay, so I've been in a pretty serious cohabiting relationship for just over 2 1/2 years now, and basically I am 100% sure that my boyfriend cheated on me, multiple times, and most likely will again. I found evidence on his Facebook while he was out at a frat party (I was using his laptop the other night, because it's nicer and I prefer it, and it was logged into his account still but he was apparently messaging some girl from his mobile Facebook app). They were very flirtatious messages, most of it coming from him. When I brought it up with him, he said it was his friend using his phone and doing that but it was only that one time (even the friend himself told me the same story, but that doesn't make it believable). Also, there were more messages from previous days that were also flirty or even straight up dirty, which he said must be someone else hacking his account. I even found a conversation with his ex that began last year, and was proof that he had been sleeping with her as recently as the beginning of this year just before she ended up pregnant. For me the biggest proof is that she even said in the messages that she was a bit worried that he might be the father of her baby. When I brought it up with him he denied it again and said it must be someone else hacking his account, which makes no sense based on her replies in the conversation. I want to know how someone can be so confident about a story that makes no sense and continue to deny something like that even though he knows that I know. Also is there any way I can get him to admit the truth?
How can I get him to admit that he cheated?
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