It's at home; I'll send you the URL I found then, but if you can't wait, I just did some searches on "box bin packing algorithm" and came up with a .c source that implements it.

The problem with picking a box based on the total volume of your component boxes is that you can't expect to pack all of your boxes perfectly into a larger one. They're arbitrarily sized and you have to assume that there are going to be some gaps in and around them.