Is an OLAP cube a duplication of data or is it just references to original tables? Or can I control it?

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It depends.

Most products duplicate the data, and require ETL to "refresh" the data, running on a regular basis but implying there is some delay between live data and OLAP data. It also implies that you can keep historical data in the cube, even if the old OLTP data is removed.

Some products will not duplicate all data, and allow to control which data is duplicated or not. That would be somehow like indexes: Some redundant data that allows for better performance, but not all the data is duplicated.

For SQL Server, for example, check the difference between MOLAP, ROLAP and HOLAP models

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