Figuring out a checksum algorithm

I've got a checksum of some kind here, some files and some checksums.

[167, 9, 4, 0, 165, 216, 39, 0] => 882
[107, 136, 2, 0, 227, 205, 39, 0] => 828

The checksum is about two magnitudes larger than the input data, so some kind of addition is likely used.  Just adding the bytes together does not work, neither does xoring the bytes with a fixed value and then adding them.

I don't think I have the means to try out whether a checksum is correct or not, and I can't generate checksums for arbritary data either.  Any ideas, some kind of common algorithm for this perhaps?

>>23
Yeah, I did give OllyDbg a shot... (actually, I think I did for an unrelated problem) but the interface is so confusing with millions of features with undescriptive names.  If there was just some nice thing that'd trace a byte from a file through the execution of the program.