Why don't modem use my new ethernet cables?

I got an Arrius modem from cox a while back. It came with a cat5e cable to connect to my computer. It works perfectly. Other cables don't work at all.

1. If I connect my modem to computer with cat5e cable - it works

2. If I connect my modem to router with cat5e cable - it works

3. If I connect my modem to computer with cat6 cable - it doesn't works

4. If I connect my modem to router with cat6 cable - it doesn't works

Is it possible my modem won't accept cat6 cables? What gives? The cables are new. I bought like 3 cat6 cables and none of them work.