If you have a suitable fixed cup wrench, there are commercial tools that will clamp it in place so you can apply a lot of force without the wrench slipping off.

I put together a home-made tool that does the same thing at negligable cost. It is a 5/8" bolt 4" long, a nut and two big washers. To use it:

1. Remove the adjustable cup, spindle and bearings. Then screw the adjustable cup back in several turns.

2. Put one washer on the bolt, feed it through the adjustable cup until it sticks out of the fixed cup, position the fixed cup wrench over the fixed cup, add a washer outside of the wrench and thread on the nut.

3. Align the wrench properly over the fix cup's flats and finger tighten the nut to hold the wrench in place.

4. Push, force, beat-on-with-mallet or do what ever in needed to break the fixed cup free.

5. Loosen the nut as the fixed cup unthreads to prevent binding. After a turn or so, the clamping bolt shouldn't be needed.

Tim's advice to use a bench vise as the fixed cup holder and the entire frame as the lever is excellent but not everyone has access to one or the space around their workbench to clear a horizontal bike frame.