Molecular diamagnetism and multicentered X-Mo-Mo and Mo-Mo-Mo interactions in hexanuclear cluster complexes [Mo(6)X(8)](n-) (X = S, Se, and Te; n = 0 and 4) are studied using calculations of nuclear independent chemical shifts (NICS) and the methods "atoms in molecules" and electron localization function. It is shown that [Mo(6)X(8)](4-) complexes are characterized by large negative NICSs related to the aromaticity of Mo-Mo bondings and to diatropic currents in Mo(6) metallic core of the cuboctahedral clusters. The calculated currents can participate in the mechanism of nucleation of the vortex lattice of macroscopic Abrikosov's electronic whirls responsible for the magnetic high-field stability of the superconducting currents in type II superconductors.