I had that book - the patterns/sequences to solve the first two layers were pretty easy to memorize, but you got to the third layer and the number of potential moves just exploded. I never did get to where I could solve the last layer without referring to the book.

Surprisingly, any initial cube configuration can be solved in 26 or fewer quarter-turns, although that wasn't proven until 2014, thirty-four years after the Rubik's Cube was released.