Is there any kind of helpful tool for looking up at the data stored on the SharePoint 2013.
I'm thinking in the lines of TreeSize or a similar program.
I'm NOT thinking of out-of-the-box SharePoint 2013 functionality.
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I never seen that kind of tool, which give you the detailed about whole farm(data stored).
But you can check the site collection wise using the SharePoint storage metrics. http://sharepointhoster.com/how-do-i-track-my-storage-usage-in-sharepoint-2013.html
Also I think also take a look of metalogix StoragePoint.
TreeSize supports scanning SharePoint Servers since V6.3, including last access / change date and the "Age of Files" and "File Type" statistics:
Full disclosure: I am the author of TreeSize Professional.