Python Program to Find Sum of Cubes of n Numbers

You can find the sum of cubes of n numbers in Python by using a loop to cube each number and add them, like sum_of_cubes = sum(i**3 for i in range(1, n+1)).

Examples

Inputn = 1

Output1

Inputn = 3

Output36

Inputn = 0

Output0

How to Think About It

To find the sum of cubes of n numbers, think of each number from 1 to n. Cube each number by multiplying it by itself twice, then add all these cubes together to get the total sum.

Algorithm

1

Get the input number n.

2

Initialize a variable to hold the sum as 0.

3

For each number from 1 to n, calculate its cube by multiplying the number by itself twice.

4

Add each cube to the sum variable.

5

After the loop ends, return or print the sum.

Code

python

n = int(input("Enter the number of terms: "))
sum_of_cubes = 0
for i in range(1, n+1):
    sum_of_cubes += i**3
print("Sum of cubes:", sum_of_cubes)

Output

Enter the number of terms: 3
Sum of cubes: 36

Dry Run

Let's trace the program for n = 3 through the code

1

Input

n = 3

2

Initialize sum

sum_of_cubes = 0

3

First iteration (i=1)

sum_of_cubes = 0 + 1**3 = 1

4

Second iteration (i=2)

sum_of_cubes = 1 + 2**3 = 1 + 8 = 9

5

Third iteration (i=3)

sum_of_cubes = 9 + 3**3 = 9 + 27 = 36

6

Output

Print sum_of_cubes = 36

i	i^3	sum_of_cubes
1	1	1
2	8	9
3	27	36

Why This Works

Step 1: Loop through numbers

We use a loop to go through each number from 1 to n to handle all numbers one by one.

Step 2: Cube each number

Cubing a number means multiplying it by itself twice, done here with i**3.

Step 3: Add cubes to sum

Each cube is added to a running total to get the final sum of all cubes.

Alternative Approaches

Using sum with generator expression

python

n = int(input("Enter the number of terms: "))
sum_of_cubes = sum(i**3 for i in range(1, n+1))
print("Sum of cubes:", sum_of_cubes)

This method is shorter and uses Python's built-in sum function with a generator for better readability.

Using formula for sum of cubes

python

n = int(input("Enter the number of terms: "))
sum_of_cubes = (n*(n+1)//2)**2
print("Sum of cubes:", sum_of_cubes)

This uses the mathematical formula that the sum of cubes of first n numbers equals the square of the sum of first n numbers, which is very efficient.

Complexity: O(n) time, O(1) space

Time Complexity

The program loops through all numbers from 1 to n once, so it takes linear time O(n).

Space Complexity

Only a few variables are used regardless of n, so space complexity is constant O(1).

Which Approach is Fastest?

Using the formula approach is fastest with O(1) time, while looping methods take O(n).

Approach	Time	Space	Best For
Loop with for	O(n)	O(1)	Simple understanding and small n
Sum with generator	O(n)	O(1)	Cleaner code for moderate n
Mathematical formula	O(1)	O(1)	Large n and best performance