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

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Javascript

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Output :

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

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

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