Abstract. We prove that the identity $(1+2+\cdots +n)^2=1^3+2^3+\cdots +n^3$ is not a coincidence but the first and simplest one of a family of multiplicative formulas involving the sums of powers of integers.

AMS Subject Classification (1991): 11B75, 11B68

Keyword(s): 11B75, 11B68

Received July 18, 2000. (Registered under 2799/2009.)