立方和与前N个自然数之和的差

给定一个整数N，找到前N个自然数的立方和与前N个自然数的总和之间的绝对差。

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

方法：

1. 前N个自然数的立方的总和，使用以下公式：
   $(N ( N + 1 ) / 2) ^ 2$
2. 前N个数字的总和，使用以下公式：
   $(N ( N + 1 ) / 2)$
3. 两者之和的绝对差为
   $S(S-1)$
   在哪里
   $S = (N ( N + 1 ) / 2)$

下面是上述方法的实现：

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 
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

// 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
 

输出：

210