1)(x+y)^3-(x-y)^3-2y=x^3+3x^2y+3xy^2+y^3-(x^3-3x^2y+3xy^2-y^3)-2y=x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3-2y=6x^2y+2y^3-2y
2)(m+n)^3+(m-n)^3-2m=m^3+3m^2n+3mn^2+n^3+m^3-3m^2n+3mn^2-n^3-2m=2m^3+6mn^2-2m
3)(a-b)^3-(c+d)^3-a+b+c+d=a^3-3a^2b+3ab^2-b^3-(c^3+3c^2d+3cd^2+d^3)-a+b+c+d=a^3-3a^2b+3ab^2-b^3-c^3-3c^2d-3cd^2-d^3-a+b+c+d
4)x^3-8+(x+2)^2-2x=x^3-8+x^2+4x+4-2x=x^3-4+x^2+2x
5)x^3-27+(x+3)^2-3x=x^3-27+x^2+6x+9-3x=x^3-18-x^2+3x