If $k(x)=\frac{x^3-512}{x-8},$ complete the table and use the results to find $\underset{x8}{lim}k(x).\frac{x}{k(x)}$

$7\mathrm{.}9$

$7\mathrm{.}99$

$7\mathrm{.}999$

$8\mathrm{.}001$

$8\mathrm{.}01$

$8\mathrm{.}1$

Complete the table.

$($Round to three decimal places as needed.$)$