I'm not sure where you got 270 GB. The article you reference states 180 TB.
Which, according to the article runs less than $10000 (180 TB * 1000 GB/TB * .048 $/GB = $8640 )
180 TB is using 4 TB drives.
270 TB is using 6 TB drives.
Backblaze uses 4 TB drives because of the increased costs and failure rates of the 6 TB drives.
https://www.backblaze.com/blog/wp-content/uploads/2015/03/bl...
(270 TB * 1000 GB/TB * .051 $/GB = $13770 )
My original estimate of $20,000 was just a rough estimate that added some padding for overhead and accessories.
http://www.ibm.com/systems/storage/tape/ts4500/index.html
The Utah Data Center has at least 100,000 square-feet of data center space. If just half of that space was used for storage then it would be over 27 exabytes worth of storage assuming a density similar to what IBM offers.
Backblaze on the other hand has their Storage Pod 4.5 which can hold up to 270 GB of storage for less than $20,000. https://www.backblaze.com/blog/storage-pod-4-5-tweaking-a-pr...