That depends on the cushion and its attachment system. Check whether the product description means the whole cushion is washable, only the outer cover is removable, or the pad is intended for spot cleaning.
These are different features. Read the care label for temperature, detergent, drying and reshaping instructions before the first wash. Take note of straps, fasteners or fitted corners so the cushion can be returned securely to its platform. Allow every part to dry fully before refitting, especially where fabric sits against wood or an enclosed bed. Do not assume that all cushions on one tree share identical care instructions. If replacements are available, confirm the model and size rather than buying a visually similar pad. A cushion that slides or overhangs can change how safely the cat enters and leaves the resting area.
Photograph the care label before washing so the instructions remain available if it fades. Check the filling separately from the cover: a removable fabric cover does not establish that its foam insert can go through the same cycle.
For product comparisons alongside this advice, see Linden wooden cat tower and Arbor Retreat. The details below explain their sizes and uses.
Further reading: cats.org.uk.
Linden wooden cat tower
Arbor Retreat
Floral Canopy