Question 633627
two special factoring formulas are two sides of the same coin: the sum and 
difference of cubes. These are the formulas:

    

{{{a^3+b^3=(a+b)(a^2-ab+b^2)}}}
   

{{{a^3-b^3=(a-b)(a^2+ab+b^2)}}}.....use this one in your case...notice that {{{a=x}}} and {{{b=y}}}

since you have {{{x^3 +64 }}}, your {{{b^3=64}}}, so you need to find a number whose cube is {{{64}}}....it is {{{4}}}, because {{{4^3=64}}}
and your expression will be {{{x^3 +64=x^3-4^3 }}}
now plug it in a rule

 {{{a^3-b^3=(a-b)(a^2+ab+b^2)}}}

 {{{x^3-4^3=(x-4)(x^2+(-4)x+4^2)}}}

or 
 
 {{{x^3-4^3=(x-4)(x^2-4x+16)}}}