How do I calculate an increase in pan sizes for a cake recipe?
Assuming the depths of the pans are all the same, then the volume will vary as the square of their linear dimensions: 


8^2 + 8^2 = 64 + 64 = 128
10^2 + 14^2 = 100 + 196 = 296
Ratio = 296/128 = 2.3125


Near enough, multiply original quantities by 2 1/3