problem given:

y=x^3, y=8 x=0, rotate about x=2

The book uses cylindrical shells given the anser

v = integral (2,0) 2pi (8-x^3)(2-x)dx

however I tried using washer getting the answer:

v=pi integral(8,0) [2-0]^2 - [y^(1/3) - 0]^2 dy

Now I know that it's incorrect, but for the life of me I can't tell why it's incorrect. Can someone help explain?