The whites are tough to keep clean. I find I have to clean my white's cages much more often than the others. (And lately, they seem to shed a lot more too!)
Depending on how bad the stains are, you can rub corn starch into the stains, let it set a few minutes and brush it out. If the satins aredark, I take a washcloth and wet it with warm water and a little vinegar. Then I try to gently work at the stain (if the rabbit is willing!). Don't "scrub" it, just take pieces of the fur and wipe it with the cloth.
Really dark stains won't come out until they shed, but you can lighten them a little.