Answer :

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


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