The intermolecular interaction that is dependent on the inverse cube of the distance between the molecules is: london force, ion - ion interaction, ion - dipole interaction, hydrogen bond

Dipole-dipole interaction depends on the inverse cube of distance between the molecules. Hydrogen bonding is an example of dipole-dipole interaction. The strength of the interaction depends on the magnitude of dipole moment of polar molecule, size of the molecule and charge and size of the ion.