The form of the final answer depends on how far you want to take the factoring.
The first step is to find the largest factor common to both terms: (x - 2y)3 .
Removing it from both terms leaves:
(x - 2y)3 [ 1 - (x - 2y)2 ]
The second term is the difference of two squares, 1 and (x - 2y)2 . It can be factored as:
[ 1 + (x - 2y)] [1 - (x - 2y)]
The interior parentheses could be removed by distributing the + and - signs across the (x - 2y) terms, but that would not simplify it much. Neither would multiplying it out.
I would suggest this as the final answer:
(x - 2y)3 [1 + (x - 2y)] [1 - (x + 2y)]