Why are you so certain it is only cultural differences, when, for example, the testing gap between the black and white children of socio-economically equally upper-middle class is persistently gaping?
I would ask how many generations those black kids' families have been in the upper-middle class. Some research has shown that it takes generations--2 or 3, at least--for "disadvantaged" people (for example, immigrants) to catch up to the achievement level of the population. If these black families are new to the middle class, it is very likely that the parents of those kids simply do not know how to effectively stimulate their children intellectually.
I would also ask if the kids in those upper-middle class black families embrace the "black" culture, which is a culture that denigrates achievement.
And so forth.
Environment plays a huge role in intellectual development. Bad nutrition, early childhood disease, and lack of intellectual stimulation all conspire to impair brain development of young children, and once that crucial developmental window is gone, the opportunity to maximize the genetic potential is lost forever.