Ahhh. I'll bet the hydraulic filter is plugged up bad and it has the wrong fluid in it! "the oil is very black, but no foam or white" Hytran should be rather thin looking (compared to other oils), lighter than 10w-30, and should be very light color, maybe even pinkish to reddish. If it's "black" then something is definitely wrong. I've had Cub Cadet tractors that may have NEVER had the transmission fluid changed, and at worst it was dark tan, maybe brown.
I'll bet that someone changed it and threw 80W90 gear lube in the differential,as that is what a typical automotive differential typically takes. GET THAT STUFF OUT OF THERE!!!!!! It WILL damage the hydraulic pump. I wouldn't even run the tractor if you can avoid it. Just open the rear differential cover and let it drain for a week or two.
Check your manual, but the number series lo-boy tractors should all have Hy-Tran in the differential and hydraulic system. Go to a Case/IH or Cub Cadet dealer and buy the correct Hy-Tran transmission fluid and a filter. It would be costly, but I would seriously consider changing the fluid and filter, running the tractor to cycle the hydraulics a bunch of times, then dump and change the fluid again. That's the only way I can think of actually getting all of it out. I may actually take three changes to get it all out, but you're probably looking at $100 to do the change 3 times. Two should get it going better. Also, remember that the only way to bleed the hydraulics to get all the air out of the system is to run the tractor and cycle the hydraulics full up/full down a BUNCH of times. Maybe as many as 50 times. So it's the same idea with the oil in the system. To fully get all the oil out, you may have to run and cycle the hydraulics a bunch.
I'll guarantee, if it's got gear lube in it, and you switch to Hy-tran, your hydraulics will work a TON faster!
1951 Farmall Cub, Cub Cadets 102, 104, 1811, 1864, Simplicity Legacy XL 4x4 Diesel with FEL, 60" mower, 50" Tiller