Question

A normal cake is divided into the maximum number of pieces, p, by c slices. When c = 1, 2, 3, 4, 5, and 6, the cake is divided into 2, 4, 8, 15, 26, and 42 slices respectively. What is the maximum number of pieces into which the cake can be divided when it is cut by 8 slices? Each slice extends across the entire cake.