I know that we have to gloom for a greatest common factor and then see if there is a sum of cubes or difference of cubes but I don't get the answer correct.

Do you mean 128u^2v^2 - 2t^2 ?

Answer: 128u^2v^2 - 2t^2 = 2(64u^2v^2 - t^2) = 2(8uv+t)(8uv-t)