It's a bit more complicated than that; not even Anthropologists can always agree on what it is...in fact, there is a complete body of study known as "Cultural Anthropology". Here's an example of one definition:
Culture…is that complex whole which includes knowledge, belief, art, law, morals, custom, and any other capabilities and habits acquired by man as a member of society (Tylor 1920 [1871]: 1)
But I agree...there are probably no circumstances under which we would all have been one race and one culture, unless you would limit our population to a few thousand people living in one spot.