It is required to find the sum 6³ + 7³ + 8³ + 9³ + 10³.

6³ + 7³ + 8³ + 9³ + 10³= Sum of cubes of natural numbers starting from 1 to 10 – Sum of cubes of natural numbers starting from 1 to 5.

Note:

Sum of cubes of first n natural numbers, 1³ + 2³ + 3³ +…..n³,

From the above identities,

Sum of cubes of natural numbers starting from 1 to 10

Sum of cubes of natural numbers starting from 1 to 5

6³ + 7³ + 8³ + 9³ + 10³ = Sum of cubes of natural numbers starting from 1 to 10 – Sum of cubes of natural numbers starting from 1 to 5.

6³ + 7³ + 8³ + 9³ + 10³ = 3025 – 225 = 2800