Find the smallest number by which 256 must be multiplied to obtain a perfect cube.

$256=\underline{2\times 2\times 2}\times \underline{2\times 2\times 2}\times 2\times 2$

Here, 2 x 2 is left after grouping numbers in triplets. Therefore, 256 is not a perfect cube. To make it a cube, we need one more 2.

In that case, $256\times 2=\underline{2\times 2\times 2}\times \underline{2\times 2\times 2}\times \underline{2\times 2\times 2}=512$ is a perfect cube.
Hence, the smallest natural number by which 256 should be multiplied to make it a perfect cube is 2.