As I understand, you want to know if it is possible to watch your TV content using a non DVR cable box from Cox on your bedroom. The Slingbox will stream the content of the device connected to it, meaning that you will be able to watch the programming of your cable box on a computer locally or remotely.
The following link will explain to you how the Slingbox works. Feel free to check it out to gather more product information:
I hope that helps. Regards.