Answer
True.
Work Step by Step
Both $n^2$ and $n^3$ are monotonic for positive $n$, meaning that they only increase as $n$ increases. Since plugging in 4 yields $80$, which is less than 100, and plugging in $5$ yields $150$, there is no solution because the function is monotonic and so there can't be solutions less than 4 or more than 5.
