You will get whatever the white is carrying. Black is simple just E/E extended black. White on the other hand in Cochins is often recessive I believe, so you'll get a bunch of black chicks, however, you'll also get whatever the white may be carrying. I've heard of several cases of barred chicks coming out of White Cochin crosses due to the White Cochin hiding barring in its genes.
I depends heavily on the varying color genes being carried by your birds but from experience I crossed a large fowl black male on white females in 2003 and came up with whites (willow legged), blacks, blacks that molted to white in the 2nd year and brown reds. Go figure on the brown reds but they were of good type and color. I have since lost all of the brown red males but still have two females from the f2 mating.
White in Cochins is recessive so unless the blacks are carrying a white gene, you wont get any Whites. They will be for the most part Black, maybe with some leakage depending on what the White is masking, and like Illia said if they are masking barring, then you can get some barred chicks.
Black is not necessarily E allele. Blacks can be built on any allele if sufficient melanizers are also present. THis means that just about any pattern or colour is possible--depending on whatever the white is masking.