I'm disassembling a bike in order to sell the frame. All has gone well until I've attempted to remove the external bottom bracket. One side unscrewed easily. The other side wont budge.

Applying more force just rounds off the grooves. The frame is alloy, the cups are FSA mega-exo. How can I remove this without damaging the frame?

Pipe wrench. And as you probably know already, the driveside cup has backwards threading, so lefty-tighty, righty-loosie (assuming English threading).

Are you turning it the right way? The right (drive side) of most current frames is left-hand threaded and the bottom bracket cup removes by turning it clockwise.

Uhh... of course I was trying to unscrew the cup the right way...

A few taps with a mallet on the end of the removal tool sorted it out.

If you ever run into one that won't come out, I have found that a large bolt with some washers on each side will get it to turn. Run the bolt through where the spindle would go with washers on both sides, run the nut on and when it gets tight, the fixed cup will turn right out.

He has one of these, though:

oops. I guess my suggestion won't work then.. I need to brush up on my reading skillz.. lol..