We need to remember that Kepler had no dynamic theory of what was going on here. This was an empirical kinematic exercise on the special case of planets orbiting the Sun.

I don't know whether or not he did a similar exercise on Jupiter's moons. Such an exercise would yield a similar equation relating the orbital period and radius, but with a different proportionality constant.

The general case would be of the form P² = KR³, with Jupiter's K being about 1,000 times that of the Sun. As a result of Newton's work we now know that K = 1/M, where M is the mass of the primary object.