Having supported and built cable modem systems for years (including them), Cox Business will do modems a few ways, but usually provisioning at the modem a limit quantity of mac/ip's (normally == 1) for what can pass, then you just *use* them as you would normally, either grabbing dhcp (with a new mac) or using statically assigning to the same public host as the main (ie firewall/router). If you get a contiguous /29 or larger network block/prefix from them or on your own, they'll usually give you a static ip and route that /29 prefix *at* your primary ip, so traffic knows how to get to you, then you just apply them with nat or however normally to the interface. They can also do private mpls connectivity, but that's another bag...
As David said, your modem is NOT a router, mostly a Layer 1-2 bridge with some provisioned security features (DOCSIS BPI), unless it's one of their combo boxes with router/wifi built-in, but those tend to suck and you don't want to use those anyways. Any routing occurs at the Cox CMTS (cable modem termination system, your cable gateway router), or your gateway firewall/router.
-mb