Cloud business intelligence is an increasingly popular choice to deliver decision support capabilities via elastic, pay-per-use resources. However, data security issues are one of the top concerns when dealing with sensitive data. In this paper, we propose a novel approach for securing cloud data warehouses by flexible verifiable secret sharing, fVSS. Secret sharing encrypts and distributes data over several cloud service providers, thus enforcing data privacy and availability. fVSS addresses four shortcomings in existing secret sharing-based approaches. First, it allows refreshing the data warehouse when some service providers fail. Second, it allows on-line analysis processing. Third, it enforces data integrity with the help of both inner and outer signatures. Fourth, it helps users control the cost of cloud warehousing by balancing the load among service providers with respect to their pricing policies. To illustrate fVSS' efficiency, we thoroughly compare it with existing secret sharing-based approaches with respect to security features, querying power and data storage and computing costs.