We explore new transition metal (TM) compound sub-nanoclusters, TM8X6 (TM = Mn, Fe, Co and X = P, B, As), using density functional theory. Their optimized geometric structures show the same polyhedral structure (tetrahexahedron) independent of a kind of TM and metalloid (X), where eight TM atoms form a cubic structure capped with six metalloid (X) atoms. Incorporating an extra TM atom into the TM cubic results in an endohedral structure, TM9X6. Encapsulation of an additional TM atom merely changes the binding energy except for the Co boride cluster. The binding energy of Co8B6 increases by incorporating an additional Co atom, in which it is observed that the electron density is accumulated between B and all Co atoms (Co atoms both at the center and at the edges), but in other clusters, the electron excess is found mainly between TM atoms. The MnnP6 (n = 8 and 9) clusters have a high adiabatic electron affinity (>6 eV) due to the relatively large difference in electronegativity between Mn and P. The highest occupied molecular orbital and lowest unoccupied molecular orbital gaps of all clusters lie in the visible range. The interaction between nanoclusters and graphene with a single vacancy is studied as a function of the different cluster landing site on the graphene, where the geometric structure change of the clusters strongly depends on the adsorption site.