# Centered cube number

Given a number n, find the n-th centered cube number.
The Centered cube number counts the number of points which are formed by a point that is surrounded by concentric cubical layers in 3D with i2 points on the square faces of the i-th layer. Source[WIKI]. Please see this image for more clarity.
The first few Centered cube numbers are:
1, 9, 35, 91, 189, 341, 559, 855, 1241, 172…………………………
Examples :

```Input :  n = 1
Output : 9

Input  : n = 7
Output : 855```

Mathematical formula for nth centered cube number is given by:

`n-th Centered Cube Number = (2n + 1)(n2 + n + 1)`

Below is the basic implementation of the above formula:

## C++

 `// Program to find nth Centered cube``// number``#include ``using` `namespace` `std;` `// Function to find``// Centered cube number``int` `centered_cube(``int` `n)``{``    ``// Formula to calculate nth``    ``// Centered cube number &``    ``// return it into main function.``    ``return` `(2 * n + 1) * ( n * n + n + 1);``}` `// Driver Code``int` `main()``{``    ``int` `n = 3;``    ``cout << n << ``"th Centered cube number: "``;``    ``cout << centered_cube(n);``    ``cout << endl;` `    ``n = 10;``    ``cout << n << ``"th Centered cube number: "``;``    ``cout << centered_cube(n);``    ``return` `0;``}`

## C

 `// C Program to find nth Centered cube``// number``#include ` `// Function to find``// Centered cube number``int` `centered_cube(``int` `n)``{``    ``// Formula to calculate nth``    ``// Centered cube number &``    ``// return it into main function.``    ``return` `(2 * n + 1) * ( n * n + n + 1);``}` `// Driver Code``int` `main()``{``    ``int` `n = 3;``    ``printf``(``"%dth Centered cube number: "``,n);``    ``printf``(``"%d\n"``,centered_cube(n));` `    ``n = 10;``    ``printf``(``"%dth Centered cube number: "``,n);``    ``printf``(``"%d\n"``,centered_cube(n));``    ``return` `0;``}` `// This code is contributed by kothavvsaakash.`

## Java

 `// Java Program to find nth Centered``// cube number``import` `java.io.*;` `class` `GFG {``    ` `    ``// Function to find``    ``// Centered cube number``    ``static` `int` `centered_cube(``int` `n)``    ``{``        ``// Formula to calculate nth``        ``// Centered cube number &``        ``// return it into main function.``        ``return` `(``2` `* n + ``1``) * ( n * n + n + ``1``);``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main (String[] args) ``    ``{``        ``int` `n = ``3``;``        ``System.out.print (n + ``"th Centered"``                         ``+ ``" cube number: "``);``        ``System.out.println (centered_cube(n));``    ` `        ``n = ``10``;``        ``System.out.print ( n + ``"th Centered"``                         ``+ ``" cube number: "``);``        ``System.out.println (centered_cube(n));``    ``}``}` `// This code is contributed by m_kit.`

## Python3

 `# Python 3 Program to find ``# nth Centered cube number` `# Centered cube ``# number function``def` `centered_cube(n) :``    ` `    ``# Formula to calculate ``    ``# nth Centered cube ``    ``# number return it ``    ``# into main function.``    ``return` `(``2` `*` `n ``+` `1``) ``*` `(``                ``n ``*` `n ``+` `n ``+` `1``)` `# Driver Code``if` `__name__ ``=``=` `'__main__'` `:``        ` `    ``n ``=` `3``    ``print``(n,``"th Centered cube "` `+``                    ``"number : "` `, ``                ``centered_cube(n))` `    ``n ``=` `10``    ``print``(n,``"th Centered cube "` `+``                    ``"number : "` `, ``                ``centered_cube(n))` `# This code is contributed by ajit`

## C#

 `// C# Program to find nth``// Centered cube number``using` `System;` `class` `GFG``{``    ` `    ``// Function to find``    ``// Centered cube number``    ``static` `int` `centered_cube(``int` `n)``    ``{``        ``// Formula to calculate ``        ``// nth Centered cube ``        ``// number & return it``        ``// into main function.``        ``return` `(2 * n + 1) * ``               ``(n * n + n + 1);``    ``}``    ` `    ``// Driver code``    ``static` `public` `void` `Main ()``    ``{``        ``int` `n = 3;``        ``Console.Write(n + ``"th Centered"` `+ ``                       ``" cube number: "``);``    ``Console.WriteLine (centered_cube(n));``    ` `        ``n = 10;``        ``Console.Write( n + ``"th Centered"` `+ ``                        ``" cube number: "``);``        ``Console.WriteLine(centered_cube(n));``    ``}``}` `// This code is contributed by aj_36`

## PHP

 ``

## Javascript

 ``

Output :

``` 3th Centered cube number: 91
10th Centered cube number: 2331```

Time Complexity: O(1)
Auxiliary Space: O(1)

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