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 $$1\leq i \leq 70.$$

(第二十五届AIME2 2007 第7题)