Tic-Tac-Toe to the Nth Dimension

In a normal 3×33 \times 3 tic-tac-toe board, there are 8 winning lines.

How many winning lines are there in a 4×4×44\times 4\times 4 tic-tac-toe board? (In this case, a winning line consists of four boxes in a row, either on the surface or inside the cube.)


Bonus: How many winning lines are there in a ndn^d tic-tac-toe hypercube, where nn is the number of cells per side and dd is the number of dimensions?

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