IR-TST 2018 Problem 5

Prove that for each positive integer $m$ , one can find $m$ consecutive positive integers like $n$ such that the following phrase doesn't be a perfect power: $$\left(1^3+2018^3\right)\left(2^3+2018^3\right)\cdots \left(n^3+2018^3\right)$$ Proposed by Navid Safaei