Bar Keeper's Friend. Wonderful all purpose cleaner.
Check out their website:barkeepersfriend.com
It cleans: porcelin, glass, fiberglass, copper, stainless steel,plastic etc. It is a wonderful product.
Mix as apaste with water. For your cups, use a toothbrush. Seconds you're done! I've found this product at Walmart for $1.70. One can will last you six month or longer. Beside vinegar, baking soda, and windex. Barkeeper's friend it about all I ever use for cleaning!
Happing cleaning! :)