Moons orbit planets and planets orbit the
Sun.  Is Kepler’s constant the same for both
circumstances?  

What Kepler's constant ? ? ! ?The only constant in Kepler's laws is in the third one, where it says something to theeffect that (square of a body's period) / (cube of its distance from the central body) is a constant.That means it's a constant for multiple little ones orbiting the same central body.But it's not the same constant for other central bodies.It's one constant for the planets, asteroids, and comets orbiting the sun.It's a different constant for the moon, TV satellites, weather satellites,and military satellites orbiting the Earth.