# Centered cube number

A centered cubic number is a number that is the sum of two successive cubes. For example, a centered cubic number. The first centered cubes are

The centered cube numbers are the spatial extension of the centered square numbers in the third dimension.

## Calculation

The te - centered cubic number is calculated according to the formula

## Relations to other figurate numbers

The te - centered cubic number is the sum of the first -centered square numbers.

## Properties

- All centered cubic numbers are odd.
- It is true, where the- th square Pyramidalzahl is:

- The sum of the reciprocals of the centered cubic numbers, so is convergent.
- The shape of centered cubes occurs in nature in the structure of atoms.

## Generating function

The function

Contains in its expansion on the left side of the equation, the result of centered cubes. It is therefore referred to as a generating function of the sequence of centered cubes.