When I 1st read this I thought, "He can't be serious..." then I read on and realized you were...okay, here goes. To begin with, "race" as a concept, is completely cultural. Other than our physical appearance, "race" does not exist, biologically speaking. Genetics has proved that the ENTIRE human race is more closely related, genetically, than one family of chimpanzees, (meaning that there is more genetic variance in that one chimp family, than there is in the entire human "race"). So, no, the "white man's brain" is not superior to the "brain" of any other race, although there are variances among individuals. "Race" as a concept is not only merely cultural, it is outdated. It is more accurate to refer to the "culture" of the African-American, (this is not "p.c." bull-crap, it's scientifically sound).
As for the matter of the cultural differences between the continent of Africa and Western Civilization, read a little history. The Egyptian culture, the Afro-Phoenicians, (the 1st of ANY civilization to sail the oceans to a large extent) the ancient Nubian culture (as old as ancient Egypt, conquered Egypt at one point, and was a vast and extremely wealthy culture in it's own right) Ancient Cush (8th c. b.c., now Ethiopia)--ever hear of the queen of "Sheba?" she was the queen of the ancient civilization of Cush, another vast and wealthy civilization in Africa. As for much of Africa's current situation, Africa is still trying to recover from the centuries (15th to early 20th century) of Western colonization, that enslaved the entire continent and exported all valuable resources. If you don't think that kind of thing would have long lasting cultural ramifications, for ANY group of people, then...well, I have no idea what to say about THAT!
What went wrong? Guns, germs, and steel. The "white man" had 'em in abundance, and it is this trifecta that allowed them to conquer the black man, the brown man, and the red man. In many ways these cultures of Africa and the Americas were more advanced, but the fact that whites had the technology of guns and the biology of disease, they were able to subjugate entire civilizations. Much of what is considered the "third world" today, is a direct result of the conquest and colonization by the Western world.
Oh, BTW, just wondering why you didn't ask this question about the people of the Americas? Why not American-Indians? The same argument you made for Africa could possibly be made for a lot of S. America as well, although it would be just as invaluable.