Sequence of Cubic Numbers and Multiplication Table

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Sequence of Cubic Numbers and Multiplication Table Cubic numbers (1, 8, 27, 64, ...) can be easily derived from a simple multiplication table trick. For example, 64 is equal to 4 times the sum of consecutive integers from 1 to 4: 1 + 2 + 3 + 4 = 10, and also equals 4 times the square of those same numbers: 4 x (1^2 + 2^2 + 3^2 + 4^2). In general, the formula n^3 can be expressed as n times the sum of consecutive integers from 1 to n, then repeated in reverse order: n x (1 + 2 + 3 + ... + (n-2) + (n-1) + n + (n-1) + (n-2) + ... + 3 + 2 + 1). This can also be rewritten as n times the square of those same numbers: n x n^2. Of course, there are many more ways to have fun with a multiplication table.