# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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; ` `} `

## 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

 ` `

Output :

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

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