The amount of multidimensional data published on the Semantic Web (SW) is constantly increasing, due to initiatives such as Open Data and Open Government Data, among others. Models, languages, and tools, that allow obtaining valuable information efficiently, are thus required. Multidimensional data are typically represented as data cubes and exploited using online analytical processing (OLAP) techniques. The RDF Data Cube Vocabulary, also denoted QB, is the current W3C standard to represent statistical data on the SW. Given that QB does not include key features needed for OLAP analysis, in previous work we have proposed an extension, denoted QB4OLAP, to overcome this problem without the need of modifying already published data. Once data cubes are appropriately represented on the SW, we need mechanisms to analyze them. However, in the current state-of-the-art, writing efficient analytical queries over SW data cubes demands a deep knowledge of standards like RDF and SPARQL. These skills are unlikely to be found in typical analytical users. Further, OLAP languages like MDX are far from being easily understood by the final user. The lack of friendly tools to exploit multidimensional data on the SW is a barrier that needs to be broken to promote the publication of such data. This is the problem we address in this paper. Our approach is based on allowing analytical users to write queries using what they know best: OLAP operations over data cubes, without dealing with SW technicalities. For this, we devised CQL (standing for Cube Query Language), a simple, high-level query language that operates over data cubes. Taking advantage of structural metadata provided by QB4OLAP, we translate CQL queries into SPARQL ones. Then, we propose query improvement strategies to produce efficient SPARQL queries, adapting general-purpose SPARQL query optimization techniques. We evaluate our implementation using the Star Schema benchmark, showing that our proposal outperforms others. The QB4OLAP toolkit, a web application that allows exploring and querying (using CQL) SW data cubes, completes our contributions.