Sounds like the centres are screwed in too tightly.
If it is a genuine rubiks storebought cube, then you could try returning it. I wouldn't bother trying to fix it though. Storeboughts have "rivited" centres with glued caps. You can't adjust the tension. You'd just end up damaging the thing.
If you can't return it, I'd either put up with it or replace it. I suggest a Diyan Guhong II. I can't give you a link as it's a competing brand, but I'm sure google is your friend here.
Please take off topic discussion off this forum. Thanks.