To be pedantic, it scales as the inverse cube to leading order as there are infinitely many higher order terms in the Taylor expansion.

(A more expanded explanation of this in words...) From potential theory the force that results from a potential is simply the gradient of the potential. We can Taylor expand the potential to make our lives easier. The resulting leading order force scales as the inverse square and this term just describes uniform acceleration that results in orbital motion. All higher order terms are the tidal force. The leading order term is usually the dominant and hence we approximate the tidal force as an inverse cube law.