Additional outlet

The fee would be a culmination of two fees.  Whatever Cox charges to install an outlet...and the construction cost to run another cable from the outside to the inside of your house, such as drilling, securing, concealing, etc.  It really depends on what you want and your options.

The demarcation point for Cox is outside your house.  There is a cable-television box attached your house.  Depending on what your want, Cox, or a contractor, would attach another coaxial cable to that box and run it to the closest exterior wall to where you want the new outlet.  Then they'll have to drill to the inside your house.

If you have a basement, they could drill into the foundation and run it across the basement ceiling to the wall.  If you have an attic, they could split the signal inside of your house, run a cable up the wall to the attic and run it down the preferred wall.  If there is already an outlet near your preferred location, such as on the other side of the interior wall, the technician could work with that.

If you want a new outlet, the biggest fee will be construction.  An alternative would be to run the cable along the baseboards.  There are concealment kits to hide and secure the cable...or you could pull off the baseboards, route the coaxial cable and reinstall the baseboards.

You should hire a contractor for suggestions and an estimate.

For your market I'm currently showing a charge of $49.99 to install an outlet on a separate trip.  -Chris