@Bruce M.: If your internet is working ok, & you don't have to do anything to maintain the working all right situation, then I would forget about it.
It may very well be that this is how it works with your cable company & Linux (Ubuntu at least). Cable is a bit different.
Your not having a router brings the question to my mind though, of what security does your ISP provide, if any? (My ignorance of cable is talking here.) When we have an ADSL modem/router, the router usually incorporates NAT or SPI which are effective firewall systems.
So I wonder if your not having a router means that the cable company is providing this (or some other) form of protection at its end?
Is your IP the same if you have a look at it from this site:
& you can also use this site to test if your computer is protected somehow:
It will also show your computers IP address which is good for verification.
If you find that your computer is unprotected then I suggest that you investigate setting up a firewall (firestarter) on your machine, if you have more than one machine you may enjoy setting up IPCop on a cheap (near enough to free these days) PII headless box. IPCop is really quite easy to set up & works like a dream.