3D Tic Tac Toe from "Building Thinking Classrooms"

This resource was made to accompany the 3D Tic Tac Toe Exercise from [b][u]Building Thinking Classrooms[/u][/b] by [url=https://twitter.com/pgliljedahl]Peter Liljedahl[/url].
THE PROBLEM:
[size=150]In a standard game of tic-tac-toe, a win occurs when 3 X’s or 3 O’s are all in a row (collinear). There are 8 ways for a win in a standard game of tic-tac-toe: 3 up and down, 3 side to side, and 2 diagonally. [b]How many ways are there to win in 3D tic-tac-toe, where the rules are the same: a win is 3 collinear X’s or O’s?[/b][/size]
This construction was made to help you visualize this problem. Drag a LARGE BLACK POINT to move a cube. Click on the point to move it up or down. Click on it again to move it to the side.
Slide the slider n above so n = 4. How many ways are there to win in a 3D-Tic-Tac-Toe game where the object of the game is to get 4 collinear X's or O's?
Slide the slider n above so n = 5. How many ways are there to win in a 3D-Tic-Tac-Toe game where the object of the game is to get 5 collinear X's or O's?
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– Tim Brzezinski

Information: 3D Tic Tac Toe from "Building Thinking Classrooms"