There is a humming noise coming from my home theater system when it is connected to my COX box.

How is your Cox STB connected to your home theater?  Humming noise very often comes from a bad ground in an analog audio circuit.  Either that or open the window and let the hummingbird out

Allen is right (if you are hooked up with analog audio.) 

As a test you can take a wire (speaker wire is fine) and touch the one end to a bare metal area on the case and the other end to the screw holding your outlet cover on. You can try the same thing on your home theater if you can find a suitable area.

This is perfectly safe assuming you haven't been shocked by your system already (the cases are supposed to be at the same voltage potential as the screw anyway. 0V - Ground) and don't go poking the wire INTO the cases. Just touch the outside.

If you get clicks, static, or even if your problem goes away you definitely have a bad ground. (Keep the volume level normal.) Unfortunately if nothing happens it doesn't prove that your ground is good or bad, so keep that in mind.

Also check that your television volume is off or muted and not creating a feedback situation.