[tex](a-b)^3-(a+b)^3=a^3 - 3a^2b + 3ab^2 - b^3-(a^3 + 3a^2b + 3ab^2 + b^3)=\\\\a^3 - 3a^2b + 3ab^2 - b^3-a^3 - 3a^2b -3ab^2- b^3=- 6a^2b - 2b^3[/tex]
[tex][(\sqrt2-1)^3-(\sqrt2+1)^3]^3=[-6\cdot(\sqrt2)^2\cdot1-2\cdot1^3]^3=[/tex]
[tex][-6\cdot2\cdot1-2\cdot1]^3=[-12-2]^3=(-14)^3=-2744[/tex]
