Have you ever dated someone cocky?

Hi so I'm currently seeing someone who is cocky and he says it's because he's knows he's about his shit and he loves himself. Which it's true, he is, but idk like he has moments where he just talks about himself all the time.

I also love myself and i know I'm also about my shit (by that i mean I'm very independent and if i really want something work hard to make it happen) but idk I've always been more humble about it. I do have those moments where i feel confident and like to show out lol but i don't spend minutes talking about how great i think i am.

I'm not a hater and i don't feel the need to knock down another person especially when they're feeling themselves but it's a little awkward for me when he starts talking about himself because i don't really know what to say. I know he's been through a lot to get to this point but does he expect me to kiss his ass or something??

Idk what would you make of this. It honestly feels sometimes like he loves talking about himself but doesn't even get the time to know me. I love myself too but i don't talk about myself in a cocky way like he does. He a very great guy, loves to take care of me, and even shows me love BUT i think that's the only issue i have.