Why wouldn't you need length? You're sorting on length. You need something to hold the spaghetti strands in an upright position, so you need volume. Volume increases faster than the material needed to bound it does.
Surface area = 6 * length^2
Volume = length^3
The more hardware you add to make the cube bigger, the much more spaghetti you can sort. The hardware increases less than O(n).
Even if other hardware components increase at O(n) (not sure of that even), because your container hardware increases at less than O(n) your total hardware increases less than O(n). You get an advantage because nature increases volume faster than its bounding lengths.
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