Same factory operators manual available at IHCubCadet.Com. There should be a 3/8" square recessed hole drain plug on the rear cover of the transmission & final drive. Oil level should be right up to the lower edge of that hole. Engine OFF. IH recommends Hy-Tran, 7 quarts to completely refill. If you drain the rearend, get a new rearend cover gasket and a filter for the hydro. Also wipe out all the accumulated residue inside the rearend that you can get to.
Two common places for Cub Cadets to leak transmission oil. First is the Hydro Gasket, IH used a cork gasket between the hydrostatic pump/motor and the rearend casting, after 15-20, sometimes 25-30 years the cork took a set and leaked oil. New Cub Cadet gasket is a buna rubber/cork composite, should last for 40-50+ years. Other leak is at outer ends of rear axle carriers. Have to remove rear cover, push axles in, remove circlips, remove axle, have to remove rear brake calipers if you have external brakes, oil seal is removed from outside of axle carrier, new oil seal tapped into casting from outside. Replace parts in reverse order that they were removed in.
The Kohler KT-17 engine originally installed in 782's was not the best engine for a garden tractor ever made, But I know many guys that can make a real strong argument that the 782 is the best garden tractor ever made by anyone.
Deere uses the similar hydro system, a Sauer-Danfoss 15U, used to be called Sundstrand, as IH used, Deere recommends their new hydraulic/transmission oil, Hy-Gard? Sauer-Danfoss says Type F ATF works also. I use Hy-Tran because I have other IH tractors.