Binding of a set of three isomeric guests (1,2-, 1,3- and 1,4-dicyanobenzene, abbreviated DCB) inside an octanuclear cubic coordination cage host H (bearing different external substitutents according to solvent used) has been studied in water/dmso (98 : 2) and CD2Cl2. These guests have essentially identical molecular surfaces, volumes and external functional groups to interact with the cage interior surface; but they differ in polarity with dipole moments of ca. 7, 4 and 0 Debye respectively. In CD2Cl2 guest binding is weak but we observe a clear correlation of binding free energy with guest polarity, with 1,4-DCB showing no detectable binding by NMR spectroscopy but 1,2-DCB having -ΔG = 9 kJ mol-1. In water (containing 2% dmso to solubilise the guests) we see the same trend but all binding free energies are much higher due to an additional hydrophobic contribution to binding, with -ΔG varying from 16 kJ mol-1 for 1,4-DCB to 22 kJ mol-1 for 1,4-DCB: again we see an increase associated with guest polarity but the increase in -ΔG per Debye of dipole moment is around half what we observe in CD2Cl2 which we ascribe to the fact the more polar guests will be better solvated in the aqueous solvent. A van't Hoff analysis by variable-temperature NMR showed that the improvement in guest binding in water/dmso is entropy-driven, which suggests that the key factor is not direct electrostatic interactions between a polar guest and the cage surface, but the variation in guest desolvation across the series, with the more polar (and hence more highly solvated) guests having a greater favourable entropy change on desolvation.