This pattern is described in the paper Scalable Component Abstractions by Martin Odersky and Matthias Zenger.

The term “Cake pattern” was coined later, in this thread: http://www.nabble.com/Inheriting-static-members-td10106162.html . Jon Pretty suggested the term ‘Cake Pattern’ because “(...) beyond my appreciation of cake, [a] cake is made of a number of layers (separated by jam), and can be sliced. The layers represent the different levels of inner class nesting. It is conceivable that you would reach the bottom layer by working your way down from the top.”