Find the sum of the following series.

16³ + 17³ + … + 35³

Given the the series S = 16³ + 17³ + … + 35³

Let S₁ = 1³ + 2³ + 3³ + … + 35³ with n = 35

Let S₂ = 1³ + 2³ + 3³ + .. + 15³ with n = 15

Required sum S = S₁-S₂

To find the sum S₁ -

Formula to find the sum of first n cubes of natural numbers is

S =

S₁ =

=

S₁ = 396900

To find the sum S₂ -

Formula to find the sum of first n cubes of natural numbers is

S =

S₂ =

=

S₂ = 14400

Required sum S = S₁-S₂

S = 396900-14400 = 382500

The sum S = 16³ + 17³ + … + 35³ = 382500