Need Answer For This Puzzle ?

I've got 2 solutions.

The trick is to think just about cube's vertical faces. I named groups of them "rings" and there are 3 such groups (around, over, over sideways), but you should also consider flipping the cube on the head (mirrored rings), so 6 rings in total per cube. Basically, every side is at the bottom/top/... once and there are 6 sides.
Then you should also think about rotating the cube around its Y-axis. I named such rotations "shifts", since the group (or list) of vertical faces shifts. There are 4 of them. But we can forget about 1st cube, because rotating it has no effect.

So that's 82944 unique stacks (6 sides, 4 possible shifts, 1st cube doesn't need to shift -> 6^4 * 4^3). Both solutions were found instantly (no delay noticed).