Question 350620
Hate to be a bearer of bad news but you didn't get it right.
.
512y^3-729
can be rewritten (as you say) as:
(8y)^3-9^3
At this point you have a "difference of cubes" -- a special case for factoring:
a^3 – b^3 = (a – b)(a^2 + ab + b^2)
.
which then gives you:
(8y - 9)((8y)^2 + (8y)(9) + 9^2)
(8y - 9)(64y^2 + 72y + 81)