My boyfriends ex keeps saying she loves him and he doesn't stop her. What do I do?

so yesterday he came to my house and he went on his phone to reply to a message and I caught a glimpse of a message his ex wrote to him. I was like oh she wrote to you? And he was like yeah but it's nothing, look. I saw that she was asking him to send her shoes (she lives in Cuba and he just got to Miami like a year ago from Cuba) but when I scrolled up I saw message after message of "i love you"s and that it'll never change and he's the love of her life etc. On the chat it looks like he didn't reply but he could've erased those messages right? He never stopped her. And he hid this from me since it's been going on for months. I feel stupid because I've had exes and guys I've talked to write to me trying to meet up again and I always tell them I have a boyfriend and to please stop. And he's there engaging in chats with this woman who he spent 6 years with. Of course I feel threatened and disrespected. He said he told her he has a girlfriend but that the Cuban women don't care and will continue especially if he's in the US, and said why am I even worried, he's here and she's there. I feel like cheating can happen without them having sex, he's cheating as soon as he has feelings for her. We had a fight and it ended with him writing to her a message to please stop writing to him those types of messages because he has a girlfriend that he cares about and to save the romantic words for "the man she is with now". he looked upset after he wrote it and that reaction makes me worry, like why is it so hard? honestly if It had been the other way around he would've been mad too. Now it's hard for me to trust him and when I'm not with him I wonder if he's talking to her. And not to brag but she has nothing on me.. I hate feeling like this, , Someone please help?
My boyfriends ex keeps saying she loves him and he doesn't stop her. What do I do?
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