I believe I understand the question. In Civ I and II, the map was a square, much like a Mercator map. There was no longitudal boundary. However, in order for a unit to move from, say, just north of Russia to just north of Canada, the unit would have to move all the way around the map, whereas in the real world (sphere) it would only have to go a little ways across the Arctic region. I think the preceding is what is meant by "cube".
I think what he means by "sphere" is for a unit to move from , say, one northern (or southern) polar coordiante square to any other northern (or southern) polar coordinate square, regardless of the intervening squares, since these squares are, in the real world, part of one continuous mass (like Antarctica).
As far as the question of whether this is incorporated into Civ III, I do not know. It'd be pretty cool, though.