A white styrofoam cup typically used in the south to drink Promethazine with Codeine cough syrup mixed with Sprite ("drank"). Possibly because of the abundance of Sonic drivethroughs in southern states which use styrofoam cups.
"I got that white cup thats full of that oil....." - Paul Wall
White cup is a term sometimes used to replace "Purple Drank or Lean." A drink popular in the south that consists of Codine cough syrup and Promethazine mixed with a soda or fruit juice. White Cup can also be used in reference to drinking "Purple Drank or Lean."
"What be your favorite drink crip." Shit you know I drink that White Cup boy!
"Yo crip, what you got in dat cup you be sippin on?" Nigga can't you see dat is a White Cup!?