How does Cognos and Business Objects work with ORACLE?

Business Objects universes are stored in the RDBMS, but in both cases, the cubes are stored externally. Cognos has its own server or desktop based PowerCubes, while Business Objects microcubes are part of a document, which can again be server based or local. These look the same regardless of which database they were sourced from, so the same tools can be used with any database (one of their strengths compared to tools from Oracle, Microsoft or IBM which are database-specific).

As for Oracle OLAP products, the long-established OFA and OSA are still based on Express, which also uses cubes based outside the Oracle database.Oracle9i OLAP Option AW does have cubes and dimensions hosted inside the database, but most Oracle products don't yet build or support such cubes and nor do most third party products (except as vanilla SQL queries).