The first third of the cube has 8 winning lines:
3 front to back
3 left to right
2 from each diagonal
You can times that by 3 to to get all of the winning lines front to back,left to right and from one diagonal to the opposite. This will equal 24.
From there, you've got from top to bottom vertically. Around the perimeter you've got 8, and in the middle you've 1, equalling 9.
Afterwards, the winning lines diagonally from the '3rd 3rd' to the '1st 3rd', a bit like the example of a winning line on the caption:
3 from the top left to the bottom right
3 from the top right to the bottom left
3 from the 'top front' to the 'bottom back'
3 from the 'top back' to the 'bottom front'
this equals 12.
Finally there are 4 winning lines from one vertex on the top to the opposite on the bottom.
Adding those totals up you have 24+9+12+4=49
Ans=49