The Hansen Solubility Parameters (HSP) for several polyhedral oligomeric silsesquioxane (POSS) compounds were successfully determined, demonstrating the applicability of the HSP approach for selected types of organic inorganic compounds. As commonly practiced with organic polymers, a set of simple "pass/fail" tests for complete solubility at a fixed concentration (100 mg/mL) was conducted for an array of five octameric POSS compounds, octa(phenethyl), octa(styrenyl), octa(isobutyl), octakis(hexafluoroisobutyl), and (1-naphthyl)heptaphenyl), and 45 test solvents. Group contributions for the octameric POSS cage were determined using three different approaches, which produced similar results. The best cage contribution estimate for the dispersive, polar, and hydrogen-bonding components, delta(D), delta(P), and delta(H) of the total solubility parameter was determined to be delta(D) = 22 (J/cc)(1/2), delta(P) = 19 (J/cc)(1/2), and delta(H) = 15 (J/cc)(1/2), with an estimated uncertainty of approximately 5 (J/cc)(1/2). The utility of the HSP approach was demonstrated by successfully identifying mixtures of poor solvents that provided significantly enhanced solubility for octa(isobutyl) POSS, and by successfully estimating the HSP of octakis(trifluoropropyl) POSS from group contributions derived solely from aromatic POSS compounds.