'Generalized' Universal Gravitation & Coulomb's Law?

Any inverse-square relation for an interaction comes from this notion of flux and flux density.

Let's say that instead of an electric field, it's just the intensity of a spherically radiating object. Let's say a 100 watt light bulb. Radiation intensity is about how much power of radiation passes through a unit of area (say meter${}^2$). So a sphere of radius $r$ surrounding that light bulb will have a total of 100 watts of power crossing the spherical boundary from inside the sphere to the outside. This means that the 100 watts is distributed equally over the entire surface area of the sphere, which is $4 pi r^2$.

So the intensity $I$, power per unit surface area, times the amount of surface is equal to the total power $P$.

$$ I cdot 4 pi r^2 = P $$

For the light bulb case above, $P$=100 watts. This makes the intensity an inverse-square quantity in our 3-dimensional space:

$$ I = frac{P}{4 pi r^2} $$

That is the root to the notion of an inverse-square law. The exponent in the denominator must be exactly 2 in a 3-dimensional space.

Now for E&M or for gravity, it is a different quantity than power that is being conserved and distributed over the surface area of a sphere of radius $r$. It is electric flux or gravitational flux that is spreading out in 3-dimensional space. Then the flux density must be an inverse-square quantity. And field strength is proportional to flux density. If you double the flux density, you also double the field strength.