My boyfriend and his ex broke up 4 months ago (she ended things with him), and we started dating three weeks later.

I felt a bit suspicious because he mentions her a lot and he looks at her instagram everyday so I couldn't help myself but ended up snooping his phone.

They've been calling at night. Usually 4-5 hours at a time till 3 am.

He's been telling her in the messages that he still has feelings for her, and that he feels like she's the one. He's also sent topless pictures of himself to her, and that he always thinks about the future with her despite her having not spoken to him in months. He says he thinks about her everyday, and even more so recently since she's been posting pictures of herself on her instagram more frequently, and that her latest picture made him think about "how much he wanted to fuck her". He told her he can't picture anything long term with me because I lack ambition and he prefers someone who is driven (she's a dentist, so is he). He asked her to meet him this weekend and she said she'd think about it.

Would this be considered cheating? What do I do?

tl;dr : boyfriend has been telling his ex he still thinks about her all the time and has feelings