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Originally Posted by petrw1

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After asking on the usenet group sci.math.numanalysis I was pointed in the right direction and was told, that the algorithm was known and used in mechanical calculators ("Friede desk calculator") in the early 60s at Boeing already. Later Hewlett Packard sold calculators such as the HP9100, which used a similiar or identical algorithm utilizing BCD (binary coded decimals).
I found this reference to the inner workings of the HP Model 9100A and the mathematical background for the algorithm. The background is that:
n
Σ 2*i  1 = n2
i=1
so it says that the sum of all 2*i1 for i starting with 1 up to n is equal to the square of n. I would be interested to learn how to write the corresponding formula for the cubic numbers, any hints?
