Silicon borides represent very appealing industrial materials for research owing to their remarkable features, and, together with other boride and carbide-based materials, have very wide applications. Various Si–B phases have been investigated in the past, however a limited number of studies have been done on the pristine SiB6 compound. Structure prediction using a data mining ab initio approach has been performed in pure silicon hexaboride. Several novel structures, for which there are no previous experimental or theoretical data, have been discovered. Each of the structure candidates were locally optimized on the DFT level, employing the LDA-PZ and the GGA-PBE functional. Mechanical and elastic properties for each of the predicted and experimentally observed modifications have been investigated in great detail. In particular, the ductility/brittleness relationship, the character of the bonding, Young’s modulus E, bulk modulus B, and shear modulus K, including anisotropy, have been calculated and analyzed.