How to cut out a box from within a larger box by all faces of the inside box? I duplicated and expanded all the faces of the inside box, then set a boolean modifier to difference on the outside box. This was in hopes it would cut lines in the outside box that lined up with all the faces of the inside one (first picture). I hid the inside box to get a look at the result and it has created a mess of diagonal lines but I can see it kinda made the shapes I wanted (image 2). Although, it did not cut the outside box and create additional faces in edit mode like I had hoped it would (image 3). What is the correct way to achieve the cut-outs that stay true to the measurements of the inside box? 

Thank you in advance.

(edit: Image 4, shows all the unwanted diagonal lines in edit mode after applying the difference modifier)
I can think of a few solutions, but the booleans and extrude came to my mind first. I would do it like this:
insect face -> extrude -> add edge -> delete faces -> cap the inner box with face -> cap the outer box -> dissolve edges after insect -> box inside of a box!