Rubik cube sequence?

[N. J. A. Sloane]

Inspired by Jaap Scherphuis's excellent web site
on generalizations of Rubik's cube,
i've added several sequences to the OEIS giving the number
of positions that are n moves away from the start in
these puzzles.  For example:

%I A079761
%S A079761 1,9,54,321,1847,9992,50136,227536,870072,1887748,623800,2644
%N A079761 Number of positions that are n moves from the starting position in the 2 X 2 X 2 Rubik cube puzzle.
%C A079761 A puzzle in the Rubik cube family. The total number of distinct positions is 3674160. A half-turn is considered to be one move.
%D A079761 D. R. Hofstadter, Metamagical Themas, Basic Books, NY, 1985, p. 359.
%H A079761 Jaap Scherphuis, <a href="http://www.geocities.com/jaapsch/puzzles/">Puzzle Pages</a>
%K A079761 nonn,fini,full,new
%O A079761 0,2
%A A079761 njas, Feb 20 2003

Does anyone know the analogous sequence for the 3 X 3 X 3 cube,
or even the beginning of that sequence?

NJAS