$ ( x + 1 )^{3} - 8 $
$ = ( x + 1 )^{3} - 2^{3} $
$ = ( x + 1 - 2 ) [ ( x + 1 )^{2} + 2 ( x + 1 ) + 2^{2} ] $
$ = ( x - 1 ) ( x^{2} + 2x + 1 + 2x + 2 + 4 ) $
$ = ( x - 1 ) ( x^{2} + 4x + 7 ) $
---------------------
$ ( x - 5 )^{3} - 27 $
$ = ( x - 5 )^{3} - 3^{3} $
$ = ( x - 5 - 3 ) [ ( x -5 )^{2} + 3 ( x - 5 ) + 3^{2} ]$
$ = ( x - 8 ) ( x^{2} - 10x + 25 + 3x - 15 + 9 ) $
$ = ( x - 8 ) ( x^{2} - 7x + 19 ) $