There are 8 corner pieces with 3 orientations each, 12 edge pieces with 2 orientations each, giving a maximum of 8!·12!·38·212 positions. This limit is not reached because:

The total twist of the cubes is fixed (3)

The total number of edge flips is even (2)

The pieces have an even permutation (2)

This leaves 8!·12!·37·210 = 43,252,003,274,489,856,000 or 4.3·1019 positions.

Total Positions

There are exactly 43,252,003,274,489,856,000 permutations, which is approximately forty-three quintillion. The puzzle is often advertised as having only "billions" of positions, as the larger numbers could be regarded as incomprehensible to many. To put this into perspective, if every permutation of a 57mm Rubik's Cube were lined up end to end, it would stretch out approximately 261 light-years.

(see related link)