Mathematical theory.

• Create a list of numbers from one to some limit,
• Remove every Nth number from the list,
• Create a new list with a rolling sum: add the numbers which were not removed in the previous step together to a new list,
• Reduce N by one and repeat the process from step 2 until you have only one number left per iteration,
• The remaining list are the original Nth powers in this range.

Example for squares

1 2 3 4 5 6  7 8  9 10 11 12
1   4   9   16   25    36

Example for cubes

1 2 3 4  5 6  7  8 9 10 11 12
1 3   7 12   19 27   37 48
1     8      27      64