Yes, and the side length of the square is the sum of the first three Natural Numbers. More Problems One of the major principles of the Mathematics Task Centre Project, is that a good problem is 'the tip of an iceberg'. Pyramid Puzzle has proved to be that, but there is more to add to its Iceberg Album. If any of the following stimulate you, then investigate, write and submit your work to this page to be added to the Pyramid Puzzle Iceberg Album. I have not once used the word proof, because I am aware that none of the propositions I have asserted have been proven.
Induction seems a likely approach.
In the July Challenging Problem I suggested using a spreadsheet to justify results. After all the sum of the first two Fourth Degree numbers is 17. This is a Prime Number which doesn't leave many options for making rectangles, even if some of the unit squares are placed on top of others to suggest a factor involving subtraction. Viggo Hartz, a Danish colleague tells me that during a Danish winter he and some children made snowball pyramids. His children discovered there is one number of snowballs which can be stacked in both shapes.