There are 9 flat and 6 diagonal planes on a 3 by 3 tic tac toe cube. How many tic tac toes can you make?

Question

I don't know how to do this

Answer 1

One each plane (draw a tic-tac-toe chart) there are

3 horizontal wins

3 vertical wins

2 diagonal wins

for a total of 8

This is the same for all 15 planes

 

15(8) = 120

Answer 2

Just to "get the picture," imagine a 3x3x3 Rubik's Cube.  How many ways can the cube be cut to produce a 3x3 grid to play tic tac toe?    3+3+3 parallel to faces and 6 that look like "half-X" on the faces.  O.K. 15.  Then, there are the cube corner-to-opposite-corner that are not on any of those planes.
 
For each grid, there are 8 possible solutions (3 rows, 3 columns, 2 diagonal).
 
On 9+6=15 planes, we have 15*8 = 120 ways to win with a 3-D tic tac toe cube.  Plus the slant diagonals.

Now, some of these are duplicates!  You need to determine how to reduce this count.