# An algebra problem by Victor Loh

Algebra Level 3

Victor knows that $2^{3} = 8 > 2^{2} = 4$ $3^{3} = 27 > 2^{3} = 8$ $4^{3} = 64 > 2^{4} = 16$ Since $4^{3} - 2^{4} = 48 > 3^{3} - 2^{3} = 19 > 2^{3} - 2^{2} = 4,$ Victor concludes that for all integers $n \geq 2$, $n^{3} > 2^{n}.$ However, his math teacher tells him that this only holds true up till a certain value of $n$, that is, when $n \geq a$ where $a$ is a positive integer, $n^{3} \leq 2^{n}.$ Find the value of $a$.

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