Question

The value of $1^3+2^3+3^3+4^3$ is _______ .

• A. $6^2$
• B. ${10}^2$
• C. 134
• D. 289

Answer 1

The correct option is B ${10}^2$

We know that the sum of cubes of consecutive natural numbers gives squares of triangular numbers.

For example:
$1^3=1^2$
$1^3+2^3=3^2$
$1^3+2^3+3^3=6^2$

Similarly, $1^3+2^3+3^3+4^3={10}^2$ where 1, 2, 3 and 4 are consecutive natural numbers and 1, 3, 6 and 10 are the triangular numbers.