Cable Modem Router

Yes.

The primary function of a router is to be able to use more than one computer, so it has nothing to do with your question.

Leaves some questions. Are we talking multiple computers ? You would normally want a router to handle the situation of multiple PCs since it will also give you additional firewall protection besides disseminating internet feed to several PCs and you could also handle wireless devices like laptops, printers, etc. A switch would also get the job done, but not as cleanly/safely. You could run two PCs off just a modem using Internet Connection Sharing in Windows and a crossover ethernet cable linking the two together - I would pop for a cheap router instead, it's a better way to go and gives you room to expand.

Expand on your situation if you want better feedback.

The answer is ... it depends ....

What are you trying to achieve?

I think the cable modem would need to be rebooted each time a different computer is used because the computers would have a different mac addr; unless one swaps the network card "as needed".

A router will be much better as one would not need to reboot the modem for the different computers used so that the "new" mac addr of the nic is recognized.

So far he hasn't even stated he has more than one computer. :)

True, then the OP didn't state that (s)he has a computer. For anyone knows, the use of the cable modem could be used for some blu-ray players that access the network for video streaming & firmware updates.

Also, the cable modem could be for the roomates' computer as the OP may not have a computer.

And a dozen other scenarios too. :)