It would be more efficient to run it at 12V instead of using an inverter. In any case, you multiply the volts by the amps on the same line. So 12V by 7 A or 120V by .72A. If you want the inverter for other things as well, the cooler will use just shy of 100 watts. If all you will use the inverter for is the cooler, a 400 watt one will provide plenty of excess capacity. I would get a pure sine wave inverter, I don't know how well the coolwe would like modified sine wave.
I have a CF110 and run it on 12V. When on a full hookup site, the converter can easily supply the 7A needed to run the cooler. We use it almost exclusively as an additional freezer since we take longer trips. But it works great as a beverage cooler when we go racing.
