#### Answer

$(4+x)(16-4x+x^2)$

#### Work Step by Step

Using $a^3+b^3=(a+b)(a^2-ab+b^2)$, or the factoring of the sum of $2$ cubes, the factored form of the given expression, $ 64+x^3
,$ is \begin{array}{l}\require{cancel}
(4+x)[(4)^2-4(x)+(x)^2]
\\\\=
(4+x)(16-4x+x^2)
.\end{array}