Create multi-level quadtree using given 128X128 matrix

As mentioned in the title, I need to make a quadtree from a 128X128 matrix, we'll call it 'A', where the parent is the sum of all values in 'A'. The children of the parent are the 4 summed values of A1 = A(1:64,1:64), A2 = A(1:64,65:128), A3 = A(65:128,1:64) and A4 = A(65:128,65:128). Of course each child is also a parent with 4 values and so on...here's a pic of what I'm describing.

I can do this the long and hard way by individually typing in every level, but this is not reasonable. I would appreciate any help in automating the building of this quadtree data structure. I have attached the 128X128 matrix (Wu.mat)