A centered cube number is a centered

Centered number

The centered polygonal numbers are a class of series of figurate numbers, each formed by a central dot, surrounded by polygonal layers with a constant number of sides...

 figurate number

Figurate number

The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes and different dimensions...

 that represents a cube

Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...

. The centered cube number for n is given by


The first few centered cube numbers are

1, 9, 35

35 (number)

35 is the natural number following 34 and preceding 36.- In mathematics :35 is the sum of the first five triangular numbers, making it a tetrahedral number....

, 91

91 (number)

91 is the natural number following 90 and preceding 92.-In mathematics:Ninety-one is the twenty-seventh distinct semiprime and the second of the form...

, 189

189 (number)

189 is the natural number following 188 and preceding 190.-In mathematics:* 189 is an odd number* 189 is a centered cube number* 189 is a composite number* 189 is a deficient number, as 131 is less than 189* 189 is a heptagonal number...

, 341, 559, 855, 1241, 1729

1729 (number)

1729 is the natural number following 1728 and preceding 1730.1729 is known as the Hardy–Ramanujan number after a famous anecdote of the British mathematician G. H. Hardy regarding a hospital visit to the Indian mathematician Srinivasa Ramanujan...

, 2331, 3059, 3925, 4941, 6119, 7471, 9009, 10745, 12691, 14859, 17261, 19909, 22815, 25991, 29449, 33201, 37259, 41635, 46341, 51389, 56791, 62559, 68705, 75241, 82179, 89531, 97309, 105525.

If is the nth centered cube number and is the nth square pyramidal number

Square pyramidal number

In mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square base...

, then


Centered cube numbers have applications in modelling the shells of atom

Atom

The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s.