Could someone please tell me the difference between the cubes created using Oracle's Analytic Workspace Manager, the cubes created in OBIEE, and the ones created in Oracle Warehouse Builder? Do these all use Oracle's OLAP functionality, or are they different things?
I think by Datawarehouse cubes, you mean the traditional relational ROLAP cubes.
It has been a long time now that OLAP engine was merged into Oracle database (starting with 9.2 version), so multidimensional MOLAP cubes can be created inside an Oracle-based DW as part of Aggregation strategy (in addition to MVs or instead of MVs) to improve query performance and simplify calculations.
Some other points.
(1). OWB can create both ROLAP cubes and MOLAP cubes. Even ODI has knowledge modules to create MOLAP (i.e., Oracle-OLAP) cubes.
(2). OBIEE cannot create Oracle-OLAP cubes in the database. I think there is some new functionality to create Essbase cubes through OBIEE, but there is no out-of-the-box functionality to create Oracle-OLAP cubes through OBIEE.
(3). The process to create Oracle-OLAP cubes using AWM and then import those into RPD is very simple. Starting with OBIEE 220.127.116.11, it understands oracle olap metadata in standard Oracle database dictionary. So when Oracle-OLAP cubes and dimensions are queried, obiee generates physical queries using OLAP_TABLE fuction, and that is how data is retrieved from OLAP engine into relational engine and then into BI server.
(4). Oracle OLAP cubes are always created in Analytical workspace, which is a table prefixed by AW$. So one quick way is to check the tables in your schema and see if there is any table with AW$ prefix.
You can also query Oracle-OLAP metadata to see what (if any) Aanalytical workspaces, MOLAP cubes and MOLAP dimensions exist in your database. Refer to Oracle OLAP Dictionary Views at http://docs.oracle.com/cd/E11882_01/olap.112/e17123/admin.htm#i1006325