My 2x2x2 rubik's cube keeps breaking? How do i fix or can I...?

My 2x2x2 popped and i was trying to put the screw back on. It didn't go on since when you put a normal screw in a hole the hole has to be a little round on the inside or swirly but it wasn't. It was permanently broken so can I try and put a 3x3x3 core in it since 3x3x3 cores don't break that easily?