Actually, it's working perfectly. On an older Cub Cadet hydro (such as yours), the brake ONLY works when the hydro lever is in the neutral position. If the lever is in forward or reverse, the brake pedal actually forces the lever back to neutral, before actuating the brakes. Sounds like yours is working fine.
Ironically, there is absolutely no use for a brake pedal on a Cub Cadet hydrostatic drive tractor. The tractor is locked in gear at all times, neutral is a braked position, meaning the machine cannot roll when the engine is on and the lever is moved to the neutral position. Actually, even when the engine is off, you have to old the hydro release lever to even roll the machine around. Brakes are worthless on hydro tractors.
If you do use the brake pedal, in an emergency, to preven running over something, you will not hurt anything, and the tractor will stop, but it's not because of the brakes, it's because the brake forced the hydro lever to the neutral position.
If you use the brake pedal all the time, to force the hydro lever to the neutral position, you'll end up wearing stuff out prematurely, and just having to replace parts that were unnecessarily worn out.
1951 Farmall Cub, Cub Cadets 102, 104, 1811, 1864, Simplicity Legacy XL 4x4 Diesel with FEL, 60" mower, 50" Tiller