No idea how to solve this problem.

We're not solving anything ....we just want to factor this as the difference of cubes

So we have

y^3 / 27    - x^9 / 216

Difference  of cubes  formula     

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

let a  = y / 3      b  = x^3 / 6       a^2  = y^2 / 9      ab  =  [y x^3 ] / 18      and    b^2 =  x^6 / 36

So we have 

( y / 3 - x^3 / 6) (  y^2 / 9  +   [y x^3 ] / 18  + x^6/ 36  )