Adrien Broner's Snapchat Tour ... Of INSANE New ATL Crib

If you thought a little thing like JAIL was gonna stop Adrien Broner from bragging ... you're wrong ... 'cause the "look at me" king has something brand new to show off ... a sick Atlanta mansion.

Broner's people tell TMZ Sports this ain't a rental -- Broner BOUGHT the $6 MILLION pad himself.

The boxer unveiled the digs to the world on his Snapchat ... showing off his foyer (with a grand staircase), outdoor dining area, office, kitchen and of course, the saltwater pool.