The forward unknown car is a 1937 Oldsmobile Series F (I think. High-mounted, bullet-shaped tail lights, trim on the side of the hood). The rearward one is a 1938 DeSoto.

There was no "huge waste of space" to justify in this building. It has a common type of design that allowed offices to be laid out so that no one was too far from windows. Look at the old General Motors Building (now Cadillac Place) in Detroit. It has a very similar design to that of the Bureau of Engraving and Printing Annex, although it is about twice as tall.

The type of architecture is common for large office buildings, apartments and hotels of the pre-air conditioned world. There are other examples in DC and other cities all over the US.

To allow ventilation and daylight to reach as many people as possible, floor plates above the main floor (or two) were kept narrow, with operable windows all around.

Jim Dandy, not sure what you are seeing as wasted space. As far as I know, the building was fully occupied with a short time of it being completed. If it's voids between the wings that you're looking at, they exist to provide light and air to all parts of the building. This is pre-A/C Washington DC, and summer can be stifling.

L to R: 1939 Buick, 1935 Oldsmobile, unknown, 1935 Ford, then a couple of VERY interesting unknowns...the sedan moving away on the right is a 1937 Dodge.

I wonder how the architect justified the huge waste of space in that building.