Round or "square"?
 

Is there any significance to the different barrel shapes with Lugers?

No Lugers were manufactured with square barrels.

I'll re-phrase then.. Flat sided barrels?

Some of the 1970s Mauser guns were made up as special order "target models" with varying barrel configurations. Some of them were of the "slab sided" type. No WWI or WWII vintage Lugers were made with other than round barrels.

You'll have to post a pic... ;)

I've seen a couple here in the forums. Thats why I asked. Thanks folks. :)