Factor the Sum or Difference of Two Cubes $512 p ^ { 3 + 1 }$

Multiple Choice

Factor the sum or difference of two cubes.
- $512 p ^ { 3 + 1 }$

A) $( 8 p + 1 ) \left( 64 p ^ { 2 } - 8 p - 1 \right)$
B) $( 8 p + 1 ) \left( 64 p ^ { 2 } - 8 p + 1 \right)$
C) $( 8 p + 1 ) \left( 64 p ^ { 2 } + 1 \right)$
D) $( 8 p + 1 ) \left( 64 p ^ { 2 } + 8 p + 1 \right)$