Número de cubo centrado

Dado un número n, encuentre el n-ésimo número de cubo centrado.
El número de cubo centrado cuenta el número de puntos que están formados por un punto que está rodeado por capas cúbicas concéntricas en 3D con i ² puntos en las caras cuadradas de la i-ésima capa. Fuente [WIKI] . Por favor vea esta imagen para mayor claridad.
Los primeros números del cubo centrado son: 
1, 9, 35, 91, 189, 341, 559, 855, 1241, 172………………………… 
Ejemplos: 
 

Input :  n = 1
Output : 9

Input  : n = 7
Output : 855

La fórmula matemática para el número de cubo centrado  en n está dada por:
 

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

A continuación se muestra la implementación básica de la fórmula anterior: 
 

// 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 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 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.

# 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# 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
// 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
?>

<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>

Producción : 
 

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

Tiempo Complejidad: O(1)
Espacio Auxiliar: O(1)