Question 227530
1331c^3 + 512d^3

I started with cube roots 11 and 8 
(11c+8d)(11c^2-(11c)(8d)+8d^2) 
You have it almost right.
= (11c+8d)[(11c)^2 - 11c*8d + (8d)^2]  Square the whole term, not just the variables.
= (11c+8d)(121c^2 - 88cd + 64d^2)