You do not understand what a modem is or what it does. A modem CANNOT route traffic, it is a bridge device... that does NOT use TCP/IP. There is NO routing table in a modem.
What you have is a "gateway" device... which combines a modem and router in one box... just like the OP.
If you want to look into this you will find that a modem uses a different protocol than transmission control protocol (TCP)...ergo a modem CANNOT route on or off a network. With a modem anything that goes in one end comes out the other end. It can ONLY bridge. (Some "modems" offer flow control and some rudimentry port blocking, but that is done before or after the modem function).
The ONLY thing a modem can do is modulate or de-modulate. End of story.
http://en.wikipedia.org/wiki/Cable_modem
http://en.wikipedia.org/wiki/Residential_gateway (In this article you will see that a gateway is sometimes referred to as a "modem" but it is in fact a modem and a router).
... so you have a "residential gateway" which IS a router.