I don't think that makes him culturally white. By that logic, having been raised by Black parents with little to no contact with my white family, I'd be culturally Black, and from your previous comment, "Do you really consider yourself Black? Black is a colour and that's not your colour," I think it's safe to say you'd agree it would be absurd to consider me culturally Black.
Regardless of who Obama was raised by, I can assure you that when he walked out the door, the "culture," society and he himself, were well aware that he was (and is) Black.
I'm sorry, but this "culturally white," or "culturally Black" thing you assert is, to my mind, something that sounds meaningful but really isn't. It reminds me of the people I encountered when I was younger, of both races, who expected me to "pick a side," to act a certain way to reflect whatever race they decided I was. It's rooted in stereotypical notions and assumptions of what Black or white culture is supposed to be. You may not have meant it that way, but that's exactly what it is in my mind.