Each federated data warehousing system contains a data warehouse and a class of data marts. Building and maintaining such systems are painful processes. In this paper, we propose our approach to improve these processes. First, a cloud-based federated data warehousing system  architecture, description of which is specified in a formal manner, is introduced. Afterwards, Unified Modelling Language (UML) is used to design the conceptual model. In this context, a cloud-based federated data warehousing application framework and its components, i.e., global  data warehouse and linked virtual data marts, as well as its services, i.e., platform-as-a-services, software-as-a-services are modelled.  Hereafter, the GAINS model is presented as an implementation example to proof of our concepts.