Factor completely. 1. x⁶-y⁶
(x–y)(x+y)(x²+xy+y²)(x²–xy+y²)

2. 2a⁷-128a
2a(a–2)(a+2)(a²+2a+4)(a²–2a+4)

Please answer both with all steps and reasons behind them. I am trying to learn math from a book and I don't understand these two questions.
For 1, I end up with (x+y)(x–y)[x²y²(x²+y²)], which is obviously incorrect from the answer above.
For 2, I end up with 2a(a³+8)(a³–8) and can't figure how to go from there.
Please help. The chapter is on polynomials and factoring, factoring special products, with lessons on perfect square trinomials, the difference of two squares, and the sum and differnece of two cubes.​