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The views and reports for Site Collections should include the content database the site collection exists in. This information is available on the dashboard but not on the detailed views and reports.
Ok, I've got your idea.
I've filed enhancement request. But at the moment to accomplish this you will need to go longer route: obtain list of site-collections as csv and expand it with content db info.
Assuming you have csv, you can use PowerShell to iterate through each of site-collections and get basic info (including content db name and sql server name) by calling REST API, documented here: http://documents.software.dell.com/DOC207759.
Here's the discussion on how to correctly use the API: http://en.community.dell.com/techcenter/sharepoint-for-all/f/4798/t/19590929.
Just for me to better understand use case: what's the original need for such information in this report? What are you trying to accomplish with adding this data into grid/csv?
Well I am planning a migration and one of the pieces of information that the customer would like to have is which database that a particular site collection is located in. They have several web applications that have multiple databases and they want to target the larger databases first. So they would like to have the content database information so they can group those site collections an prioritize them correctly.
This information is available on the dashboard and shows right below the Site Collection name so it must be available. Would just like to have this same information on the detailed view so I can export to a csv.