Vincent’s Hollow Cube Theorem

March 26, 2023

If you want to hollow a 3 by 3 rubiks cube, you take out the one cube in the center.

But if you want to hollow a 4 by 4 rubiks cube how do you know what to take out? Well, here you go! Since 64 is the 4 by 4 cube, and 8 is the 2 by 2 cube, so, 64–8=56! You take out 8 cubes. The hollow cube is 56.

So what is the equation.

number of cubes³ – (number of cubes – 2 ) ³

If you have a 5 by 5 rubiks cube, you cube the number then subtract 2 and then cube that. So, it will be 125 [which is 5 cubed], minus 27 [which is 3 cubed]. How did you get 3, you subtract 2 from 5. So it is the number cubed minus the number–2 cubed.

But it doesn’t work for cube numbers 1 and 8 if you are using whole numbers because you can’t subtract 2 from the cube roots 1 and 2. So it only works on all rubiks cubes bigger than 3 by 3 up to infinity.

Here are the first 5 Vincent hollow cube numbers:

Rubiks cube size             math              Hollow cube total 

3                    3 cubed minus 1 cubed           26 

4                    4 cubed minus 2 cubed           56 

5                    5 cubed minus 3 cubed           98 

6                    6 cubed minus 4 cubed           152 

3                    7 cubed minus 5 cubed           218