If you have a fixed cup wrench or access to one, here is an alternative to Sheldon's tool that is easier on the cup races.
Buy a 4" long 5/8" bolt, two large diameter thick washers and a nut.
Remove the adjustable cup, spindle and bearings, then thread the adjustable cup back in several turns. Put one washer on the bolt and stick it through the adjustable cup and out the hole in the fixed cup. Place your fixed cup wrench over the bolt, add the second washer and the nut. Align the wrench on the cup's flats and tighten the nut finger tight so the washer holds the wrench firmly in place. Apply force or even a mallet to the wrench to break the cup free. As SOON as it moves even a little. begin to back out the nut to allow the cup to unthread. After a turn or so, you should be able to remove the bolt assembly and remove the cup by hand.