Kepler's third law states that the square of the period of the orbit is directly proportional to the cube of the radius of the orbit (T^2=kr^3) where r is some constant to be determined. This can be determined using:

Newton's law of gravitation: F=GMm/r^2 Centripetal Force: F=mw^2r, where w is the angular velocity in rad/s.

By equating these 2 equations and cancelling out any terms possible we arrive at GM=r^3w^2.
The angular velocity can be described as the angle a body has travelled through in a period of time. Assuming a full circular orbit this would be equal to 2*pi radians in a period of T. Therefore w=2*pi/T. This can be substituted in to obtain T^2=(4*pi^2/GM)*r^3. Therefore the constant of proportionality equals 4pi^2/GM.