This paper presents a data-agnostic testing technique for multi-dimensional databases (OLAP cubes), with a fault-model, a test-coverage-model, a test automation technique and a technique for tests generation. The test generation is mostly suitable for systems with little or no transformation between the data loaded from the source, relational system and the data loaded into the target, analytical one, while the faults and coverage model discussions are broadly applicable. We present the main design considerations for the proposed testing approach and describe the implementation of the framework for test automation and of the test generation tool. The gains in tests maintainability, reliability and failure analysis effort are assessed in comparison with a record-and-replay technique using as show-case the test suites for the OLAP cubes delivered out-of-the-box with the Business Intelligence modules of the Microsoft Dynamics AX® Enterprise Resource Planning system.