Which one of the following is the difference of the sum of cubes of first ten natural numbers

Which one of the following is the difference of the sum of cubes of first ten natural numbers and the sum of squares of first ten natural numbers?

1. 2400
2. 2640
3. 2880
4. 2000

• Answer: The correct option is B
• Explanation:

  Sum of cubes of first 10 natural numbers

  $$ \left( \frac{n(n+1)}{2} \right)^2 = \left( \frac{10 \times 11}{2} \right)^2 = 55^2 = 3025 $$

  Sum of squares of first 10 natural numbers

  $$ \frac{n(n+1)(2n+1)}{6} = \frac{10 \times 11 \times 21}{6} = \frac{2310}{6} = 385$$

  Difference = 3025 - 385 = 2640