Cheating Bastard

Hello everyone I am in a very difficult situation. I have been with my partner for 5 years and engaged for 1 year. I recently found out 2 days ago that he was cheating on me with a girl he told me before not worry about. I confronted him about it and he confessed that he did cheat on me with this girl for 1 month, and he keeps telling me it was a mistake, but a mistake for me is having a one night stand with someone else and never seeing them again, not being with someone else and being with me at the same time. What makes this difficult is that we have a 3 month old baby boy and my emotions are everywhere. I feel like I want to work it out but can't stop thinking about it, because he tells me that he loves me and care for me but how can you do that to someone you love and care about that's what I can't wrap around my head around it. Ladies what would you do in my situation? BTW he states this happened 2 years ago but I found the last message he wrote was last year in September two month before I got pregnant with our baby.