cheating?

Backstory: they talked before we dated and he had feelings for her and so did she, but she had a boyfriend, but they didn't care, they continued to talk. And I've caught him texting her 3 times now. My boyfriend of 8 months had been contacting his "ex" or crush for over a month and never told me. The night that I asked if he texted anyone through social media, he said "no" then later with guilt told me they've been texting for a month. Idk if it was intimate or not, but they were still texting and he started to ignore me throughout all those times, but he still doesn't want to break up and he promises that he would stop lying to me and will never talk to her again. Would this count as cheating? Should I believe him? Should I go back to him?