User blog:ArtismScrub/3D Sudoku idea

This isn't strictly related to googology, more to mathematical puzzles.

Right now I'm only posting this here because A) this is the most popular mathematics wiki on Fandom afaik, B) I haven't posted here in around a year, and C) I don't think anyone cares.

How the game works.
While normal Sudoku is a 9*9 planar array of numbers 1-9, 3D Sudoku is a 9*9*9 cubic array of symbols 0-9 and A-Q (base 27).

Instead of being split up into 3*3 squares, vertical and horizontal lines, the splits in 3D Sudoku are... more complicated.

Each possible 9*9 square is split into three 3*9 rectangles (on both applicable axes), and each possible 3*9 rectangle must contain one of each symbol 0-Q, none repeated. Additionally, each 3*3*3 cube (of which there are 27) must contain one of each symbol 0-Q, none repeated.

Questions
Mathematical questions: Possibly more subjective questions:
 * How many possible solutions are there to a 3D Sudoku cube?
 * How many partial 3D Sudoku grids are there, such that there can only be one solution with all the givens?
 * How would you recreate this as a playable computer program?
 * Is this humanly solvable with a reasonable number of givens?