Verified answer

Sum of two cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Difference of two cubes: a^3 - b^3 = (a - b)(a^2 + ab + b^2)

x^3 + 8y^3

(x + 2y)(x^2 - 2xy + 4y^2) <===

x^9 - 27y^6

(x^3 - 3y^2)(x^6 + 3x^3y^2 + 9y^4) <===

use this

a^3+b^3 = (a+b)(a^2-ab+b^2) and,

a^3-b^3 = (a-b)(a^2+ab+b^2) and

=x^3+8y^3

=x^3+(2y)^3

=(x+2y)[x^2-xy+(2y)^2]

=(x+2y)[x^2-xy+4y^2]

=x^9 - 27y^6

=(x^6)^3 - (3y^2)^3

=[(x^6) - (3y^2)][(x^6)^2+(x^6)(3y^2)+(3y^2)^2]