$ x^{3} + 6x^{2} + 12x + 8 - 27y^{3} $
$ = x^{3} + 3 . x^{2} . 2 + 3 . x . 2^{2} + 2^{3} - 27y^{3} $
$ = ( x + 2 )^{3} - ( 3y )^{3} $
$ = ( x + 2 - 3y ) [ ( x + 2 )^{2} + 3y ( x + 2 ) + ( 3y )^{2} ]$
$ = ( x - 3y + 2 ) ( x^{2} + 4x + 4 + 3xy + 6y + 9y^{2} ) $