So,a six inch core of ice represents billions and billions of cubic feet of atmosphere? Uh huh...
Not sure where you got that idea.
From the article...
In addition to collecting 3,405 meters (11,160 feet) of a 12.2-centimeter (4.8-inch) diameter ice core, a new directional-drilling procedure was developed that allowed the team to drill through the wall of the main hole and collect a total of 285 meters (936 feet) of additional core from five of the most scientifically interesting time periods. This enables replication of the results and expands the suite of measurements that can be made on the most interesting ice.