Statistical data is one of the most important sources of information, relevant to a large number of stakeholders in the governmental, scientific and business domains alike. A statistical data set comprises a collection of observations made at some points across a logical space and is often organized as what is called a data cube. The proper definition of the data cubes, especially of their dimensions, helps processing the observations and, more importantly, helps combining observations from different data cubes. In this context, the Linked Data principles can be profitably applied to the definition of data cubes, in the sense that the principles offer a strategy to provide the missing semantics of the dimensions, including their values. In this thesis we describe the process and the implementation of a mediation architecture, called OLAP2DataCube On Demand, which helps describe and consume statistical data, exposed as RDF triples, but stored in relational databases. The tool features a catalogue of Linked Data Cube descriptions, created according to the Linked Data principles. The catalogue has a standardized description for each data cube actually stored in each statistical (relational) database known to the tool. The tool offers an interface to browse the linked data cube descriptions and to export the data cubes as RDF triples, generated on demand from the underlying data sources. We also discuss the implementation of sophisticated metadata search operations, OLAP data cube operations, such as slice and dice, and data cube mashup operations that create new cubes by combining other cubes.