Answer
$(4x+1)(16x^{2}-4x+1)$
Work Step by Step
$ 64x^{3}+1\qquad$...use the sum of two cubes:
$\mathrm{A}^{3}+\mathrm{B}^{3} = (\mathrm{A}+\mathrm{B})(\mathrm{A}^{2} - \mathrm{A}\mathrm{B} + B^{2})$
$=(4x)^{3}+1^{3}$
$=(4x+1)(16x^{2}-4x+1)$