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Difference between Sum of Cubes and Sum of First N Natural Numbers
  • Last Updated : 24 Feb, 2021

Given an integer N, find the absolute difference between sum of the cubes of first N natural numbers and the sum of first N natural numbers.
 

Input: N = 3
Output: 30
Sum of first three numbers is 3 + 2 + 1 = 6
Sum of Cube of first three numbers is = 1 + 8 + 27 = 36
Absolute difference = 36 - 6 = 30

Input: N = 5
Output: 210

 

Approach: 
 

  1. The sum of the cube of first N natural numbers, using the formula: 
    (N ( N + 1 ) / 2) ^ 2
     
  2. The sum of first N numbers, using the formula: 
    (N ( N + 1 ) / 2)
     
  3. The absolute difference between both the sums is 
    S(S-1)
    where 
    S = (N ( N + 1 ) / 2)
     

Below is the implementation of the above approach:
 

C++




// C++ program to find the difference
// between the sum of the cubes of the
// first N natural numbers and
// the sum of the first N natural number
 
#include <bits/stdc++.h>
using namespace std;
 
int difference(int n)
{
 
    int S, res;
 
    // Sum of first n natural numbers
    S = (n * (n + 1)) / 2;
 
    // Find the required difference
    res = S * (S - 1);
 
    return res;
}
 
// Driver Code
int main()
{
    int n = 5;
    cout << difference(n);
 
    return 0;
}


Java




// Java program to find the difference
// between the sum of the cubes of the
// first N natural numbers and
// the sum of the first N natural number
 
class GFG
{
 
static int difference(int n)
{
 
    int S, res;
 
    // Sum of first n natural numbers
    S = (n * (n + 1)) / 2;
 
    // Find the required difference
    res = S * (S - 1);
 
    return res;
}
 
// Driver Code
public static void main(String[] args)
{
    int n = 5;
    System.out.print(difference(n));
}
}
 
// This code is contributed by 29AjayKumar


Python3




# Python3 program to find the difference
# between the sum of the cubes of the
# first N natural numbers and
# the sum of the first N natural number
def difference(n) :
 
    # Sum of first n natural numbers
    S = (n * (n + 1)) // 2;
 
    # Find the required difference
    res = S * (S - 1);
 
    return res;
 
# Driver Code
if __name__ == "__main__" :
 
    n = 5;
    print(difference(n));
     
# This code is contributed by AnkitRai01


C#




// C# program to find the difference
// between the sum of the cubes of the
// first N natural numbers and
// the sum of the first N natural number
using System;
 
class GFG
{
static int difference(int n)
{
    int S, res;
 
    // Sum of first n natural numbers
    S = (n * (n + 1)) / 2;
 
    // Find the required difference
    res = S * (S - 1);
 
    return res;
}
 
// Driver Code
static public void Main ()
{
    int n = 5;
    Console.Write(difference(n));
}
}
 
// This code is contributed by ajit


Javascript




<script>
// JavaScript program to find the difference
// between the sum of the cubes of the
// first N natural numbers and
// the sum of the first N natural number
   
    function difference(n)
    {
   
        let S, res;
   
        // Sum of first n natural numbers
        S = Math.floor((n * (n + 1)) / 2);
   
        // Find the required difference
        res = S * (S - 1);
   
        return res;
    }
   
    // Driver Code
 
    let n = 5;
    document.write(difference(n));
  
//This code is contributed by Surbhi Tyagi
 
</script>


Output: 

210

 

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