As publishing copyrighted material on the internet without the permission of the owner is against the law, you must remove all copyrighted material from your server as soon as you get notified about it.
You should have TOS with clear information about copyright issues. It's up to you whether you give the user a 2nd chance or cancel his account as he has acted against your TOS.
When your server gets known as a source of copyrighted material and you don't act in a responsible way, you can get into trouble and they may even shut down your server.
As you've got already several complaints you should really monitor your accounts very closely and select your users more carefully to avoid further complaints.
**This is just my personal opinion and should not be considered as legal advice**