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 <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;
}

C

// C Program to find nth Centered cube
// number
#include <stdio.h>

// 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

<?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)