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Centered Cube Number

CenteredCubicNumber

A figurate number of the form,

CCub_n=n^3+(n-1)^3=(2n-1)(n^2-n+1).

The first few are 1, 9, 35, 91, 189, 341, ... (OEIS A005898). The generating function for the centered cube numbers is

(x(x^3+5x^2+5x+1))/((x-1)^4)=x+9x^2+35x^3+91x^4+....

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