Sum of First n Terms

Problem

Given an integer n, calculate the sum of series $1^3 + 2^3 + 3^3 + 4^3 + …$ till n-th term.

Examples:

Example 1:

Input:
n=5
Output:
225
Explanation:
1^3+2^3+3^3+4^3+5^3=225

Example 2:

Input:
n=7
Output:
784
Explanation:
1^3+2^3+3^3+4^3+5^3+6^3+7^3=784

Your task:

You don't need to read input or print anything. Your task is to complete the function sumOfSeries() which takes the integer n as a parameter and returns the sum of the cubes of the first n natural numbers.

• Expected Time Complexity: $O(1)$
• Expected Auxiliary Space: $O(1)$

Constraints:

• $1<=n<=50000$

Solution

Python

def sumOfSeries(self,n):
    sum_cubes = (n * (n + 1) // 2) ** 2
    return sum_cubes

Java

long sumOfSeries(long n) {
    long sum_cubes = (n * (n + 1) / 2) * (n * (n + 1) / 2);
    return sum_cubes;
}

C++

long long sumOfSeries(long long n) {
    long long sum_cubes = (n * (n + 1) / 2) * (n * (n + 1) / 2);
    return sum_cubes;
}

C

long long sumOfSeries(long long n) {
    long long sum_cubes = (n * (n + 1) / 2) * (n * (n + 1) / 2);
    return sum_cubes;
}

• Time Complexity: $O(1)$
• Auxiliary Space: $O(1)$