Router

My router plugs into a port that also has the cable box plugged in to it. There are 2 ports in the plug that goes into the wall, one has the cable box in it, one with the router plugged in. I was wondering if the cable box needs the router plugged into the connector, or if I can move my router to another part of the house that has the required wall port so it can be more centralized in my house.

Thanks,

Jane