We're kind of over thinking this here.
For an extension cord, it's really the length, as well as the awg, that you're looking at.Hopefully the OP already has what he needs.
Under 25', a 16awg extension cord will run that router just fine. Longer than 25' and you would want to consider stepping up to 14awg.
I would be willing to bet that the internal wiring, and provided cords, on the largest routers on the market is probably 16awg internally, and 14awg for the cord, at best.
"The first thing you need to know, will likely be the last thing you learn." (Unknown)