rfreddy321:
Welcome to Flyertalk!
I have not flown to CUN from any of the DC airports yet so I can't provide you a trip report about the route you are inquiring about. However, if you do some research, you will find that there are a number of airlines that will fly business class from the area airports to CUN, with DL having the most number of flights, FL flying nonstop from BWI to CUN and UA flying nonstop from IAD to CUN. There are fewer carriers flying "F class" on these routes, with US having the only one stop F service using 767 wide-body planes connecting from CLT and UA having the only nonstop service from IAD to CUN.
Good luck and have fun exploring the flight opportunities. Please let us know the itinerary you finally come up with.