There are two types of what I call powerful words:
whole words whose letter totals (assigning a=1, b=2, ... z=26) are a square, a cube etc.
words which break into a series of letter groups each of whose total is a square, cube etc.
Let us begin by taking a look at the first of these types of powerful word. Unreferenced words are in the OED, Second Edition. Sources of non-OED words are given at the end.
Word Ways: Vol. 35
, Article 11.
Available at: http://digitalcommons.butler.edu/wordways/vol35/iss3/11