How do you remove black rubber marks from white painted furniture

Try nail polish remover and a small piece of 3M kitchen scrubber pad, and if necessary paint thinner. And if all else fails, paint over it with white paint. Any 'remover' product will smudge it around no matter what. And ruin the 3M pad.

Actually it depends on the type of the paint used on your furniture like oil paint, distemper, plastic PVC paints, polymer paint etc

Furthermore refer the below video resource link for more specific ideas.

How to Remove Stains from Wood Furniture (http://www.howcast.com/videos/173030-How-to-Remove-Stains-from-Wood-Furniture)

Are we talking about the wood, or wannabe wood on the furniture? If so, covering it with another coat of white paint is likely the best option.

Sadly I have heard of people that have painted leather, or other material. If that's the case here, it may be time to replace the furniture.

I would try gently scrubbing with a magic eraser, (or the generic version from walmart!)

A non-abrasive cleanser like Bonami might work as well.

Mineral spirits and 0000 steel wool.

I will first find the maintenance guiding of the furniture, usually there is method for such thing.

I have worked in Furniture for 50 yrs try automotive wax or compound