@.AV. 

Although Archer C6 is a gigabit router (1Gbps for each port) and there's no point to use higher than Cat5e to connect to another gigabit or faster device, you can use Cat8 as well.

" One of the great things about Cat 8 cable is the backwards compatibility it provides. Just like Cat5e, Cat6, Cat6a, and Cat7 cabling, Cat8 Ethernet Cable uses RJ45 connectors making it fully backward compatible. Backward compatibility feature will support all of your existing devices. "

Ref - https://satmaximum<dot>com/cat8-ethernet-cable-the-future-of-networking-cables.html