Let t-2=x
Let t+2=y
Therefore, you have
x^3 + y^3
= (x + y)(x^2 - xy + y^2) Now sub in original values
= (t-2 + t+ 2)(t^2 - 4t + 4 - (t^2 -4) + t^2 + 4t + 4)
= 2t(t^2 + 12)
And thats it. Not hard really, except typing it out on a computer. Same asnwer as above, but with working.