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Python Program to Find the Sum of Squares of the First N Numbers

Beginner · Numbers

This program adds up the squares of the first n natural numbers, 1^2 + 2^2 + 3^2 and so on up to n^2. For n = 5 that is 1 + 4 + 9 + 16 + 25 = 55, and the answer is checked with the formula n(n + 1)(2n + 1) / 6.

Program

sum_of_squares.py
n = 5 # or: n = int(input("Enter n: "))
total = 0
terms = []
for i in range(1, n + 1):
total += i * i
terms.append(str(i * i))
print(" + ".join(terms), "=", total)
print(f"Sum of the squares of the first {n} numbers: {total}")
# The formula gives the same answer without a loop
formula = n * (n + 1) * (2 * n + 1) // 6
print("Using the formula:", formula)
Output
1 + 4 + 9 + 16 + 25 = 55
Sum of the squares of the first 5 numbers: 55
Using the formula: 55

How it works

  1. The loop runs i from 1 to n and adds i * i, the square of i, to total.
  2. Each square is also saved as text in terms, so " + ".join(terms) can print the whole sum.
  3. The formula n * (n + 1) * (2 * n + 1) // 6 gives the same result in one step, however big n is.
  4. The product is always divisible by 6, so // gives the exact whole number.

Other ways to write it

Using sum() and a generator

Using sum() and a generator
n = 10
total = sum(i ** 2 for i in range(1, n + 1))
print(f"Sum of the squares from 1 to {n}: {total}")
Output
Sum of the squares from 1 to 10: 385

sum() adds up the squares as the generator produces them, without building a list first.

Sum of cubes

Sum of cubes
n = 5
cubes = sum(i ** 3 for i in range(1, n + 1))
square_of_sum = (n * (n + 1) // 2) ** 2
print("Sum of the cubes from 1 to", n, "is", cubes)
print("Square of the sum 1 to", n, "is", square_of_sum)
Output
Sum of the cubes from 1 to 5 is 225
Square of the sum 1 to 5 is 225

The sum of the first n cubes always equals the square of the sum of the first n numbers: here both are 225.

Try it yourself

Find the difference between the square of the sum and the sum of the squares for the first 10 numbers.

Edit the program above and press Run, or open it in the full editor to save it and share it. To watch it run line by line, open it in the visualizer.

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