# 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 i^{2} 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)(n^{2}+ n + 1)

Below is the basic implementation of the above formula:

## C++

`// Program to find nth Centered cube` `// number` `#include <bits/stdc++.h>` `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;` `}` |

## 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

`<?php` `// Program to find nth` `// Centered cube number` `// Function to find` `// Centered cube number` `function` `centered_cube(` `$n` `)` `{` ` ` `// Formula to calculate nth` ` ` `// Centered cube number &` ` ` `// return it into main function.` ` ` `return` `(2 * ` `$n` `+ 1) *` ` ` `(` `$n` `* ` `$n` `+ ` `$n` `+ 1);` `}` `// Driver Code` `$n` `= 3;` `echo` `$n` `, ` `"th Centered cube number: "` `;` `echo` `centered_cube(` `$n` `);` `echo` `"\n"` `;` `$n` `= 10;` `echo` `$n` `, ` `"th Centered cube number: "` `;` `echo` `centered_cube(` `$n` `);` `// This code is contributed by m_kit` `?>` |

## Javascript

`<script>` `// Program to find nth Centered cube` `// number` `// Function to find` `// Centered cube number` `function` `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` `let n = 3;` `document.write(n + ` `"th Centered cube number: "` `);` `document.write(centered_cube(n));` `document.write(` `"<br>"` `);` `n = 10;` `document.write(n + ` `"th Centered cube number: "` `);` `document.write(centered_cube(n));` `// This code is contributed by rishavmahato348.` `</script>` |

**Output :**

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

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

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