So you're saying it's a 9x9x9 cube, such that every 9x9 slice through it in any direction is a valid 2D Sudoku grid?

That's interesting, and different from the only other suggestion I've heard for 3D Sudoku. Since 2D Sudoku is a grid N^2 entries across, it seemed obvious that 3D Sudoku would have to be N^3: so for the usual N=3, you'd have a 27x27x27 cube, with every number from 1 to 27 appearing once in every row, once in every column, once in every row-in-the-other-direction, and once in every 3x3x3 sub-cube. Of course this would make N=3 rather unwieldy, so dropping down to N=2 and an 8x8x8 cube would probably be more sensible.

The version you describe seems somehow less "truly" 3-D, since there's no block constraint based on three-dimensional cubelets. It reminds me very much of the sense of letdown I experienced on seeing the "official" 3-D sequel to Tetris, Welltris. It seemed obvious to me that the right way to do 3-D Tetris was the way Block Out did it.

Ideally, though, it would be nice to find a form of 3-D puzzle which had all of 1-D (row and column), 2-D (subsquare in a single plane) and 3-D (subcube) constraints. I fear there's no way to do that, though.

(I don't see any need to update my solvers, incidentally: they're not there so I can cheat at published Sudoku puzzles, they're there as part of the necessary mechanism for automatically generating my own. Unless I plan to generate 3D puzzles myself, there's no need to bother.)

So you're saying it's a 9x9x9 cube, such that every 9x9 slice through it in any direction is a valid 2D Sudoku grid?

Yep. I also felt the same disappointment that there's no constraint on the 3x3x3 sub-cubes.