I have had various cable modems over the years, all of which were on cable based networks, and I have had as many as 4 computers hanging off of a switch, and everything has worked fine. It seems that 4 computers connected to a switch that has a port labeled as "Internet" knows where the world is, and routes everything that isn't a local machine to the "Internet".
I would not go without a router if I needed more than a single switch, but what I have done has worked for me.