Molecular diamagnetism and multicentered X-Mo-Mo and Mo-Mo-Mo interactions in hexanuclear cluster complexes [Mo6X8](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 [Mo6X8](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.