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