If you have the Image Processing Toolbox, you can use blockproc
blockproc(magic(100),[10 10],@(bs)sum(bs.data(:)))
And for more info:
doc blockproc
Otherwise just use a double for-loop.
OR if you're curious to learn about vectorizing and speed is a top priority:
G = reshape(sum(reshape(sum(reshape(A,sz(1),blk(2),[]),2),blk(1),[]),1),sz./blk);
And broken into pieces:
A = magic(100);
blk = [10 10];
sz = size(A);
B = reshape(A,sz(1),blk(2),[]); %reshape so every blk column is a page
C = sum(B,2); %sum blocks across rows
D = reshape(C,blk(1),[]); %reshape so each column is a block
E = sum(D,1); %sum columns
F = reshape(E,sz./blk); %reshape to final size.
