Do your cats eat bugs?

My cat eats bugs,spiders,roaches and even lizards and squirrels. She's left a few squirrel parts all over the yard and even baby rabbits She is so mean killing little baby bunnies. Anyways I think she does it to get them out of her yard, she stays healthy eating stuff outside and is fat from eating things outside. We of course give her kitty food but she doesn't really eat it, anyways she'll swallow the bugs after she kills them. My dog however will chase the bugs as well and kill them to protect me, I love my animals they are so sweet.