Question

The sum of cubes of first five consecutive numbers starting from one is a perfect square of a number. Find the number.

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Answer 1

We can observe the pattern accordingly:
$1^3$ + $2^3$ = 9 = $3^2$
$1^3$ + $2^3$ + $3^3$ = 36 = $6^2$
$1^3$ + $2^3$ + $3^3$​ + $4^3$​ = 100 = ${10}^2$
$1^3$ + $2^3$ + $3^3$ + $4^3$ + $5^3$ = 225 = ${15}^2$