Factor completely 512x^3+2197y^3

Rewrite 512x^3 as (8x) ^3

(8x) ^3 + 2197y^3

Rewrite 2197y^3 as (13y) ^3

(8x) ^3 + (13y) ^3

Since both terms are perfect cubes, factor using the sum of cubes formula.

a^3 + b^3 = (a + b) (a^2 - ab + b^2) where a = 8x and b = 13y.

(8x + 13y) ((8x) ^2 - (8x) (13y) + (13y) ^2)

Simplify

(8x + 13y) (64x^2 - 104xy + 169y^2)