2007 AIME II Problem 7

Given a real number x, let \lfloor x \rfloor denote the greatest integer less than or equal to x. For a certain integer k, there are exactly 70 positive integers n_{1}, n_{2}, \ldots, n_{70} such that k=\lfloor\sqrt[3]{n_{1}}\rfloor = \lfloor\sqrt[3]{n_{2}}\rfloor = \cdots = \lfloor\sqrt[3]{n_{70}}\rfloor and k divides n_{i} for all i such that 1 \leq i \leq 70.

Find the maximum value of \frac{n_{i}}{k} for 1\leq i \leq 70.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.