We propose a novel framework, Multi-OBDM, that extends ontology-based data management (OBDM) by treating multidimensional data cubes and hierarchies as first-class constructs. In our framework, these components are intentionally defined over a domain ontology, which is connected to operational data sources through mappings, in accordance with the OBDM paradigm. This design explicitly and formally clarifies the relationship between aggregated data and the underlying individual-level data, while preserving a declarative specification of data lineage. Furthermore, we introduce essential reasoning services tailored to multidimensional entities, including various types of analysis and quality assessment tasks, as well as query answering.