A

Step 1: Understand Kepler's Laws. Kepler's first law states that the orbits of planets are elliptical with the sun at one focus. Kepler's second law (law of areas) states that a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time.
Step 2: For the inverse cube law, the gravitational force acts as a central force and can cause similar symmetry as gravitational force with an inverse square law. The conservation of angular momentum still applies, which supports Kepler's second law (law of areas).
Step 3: Kepler's third law relates the square of the period of orbit to the cube of the semi-major axis of the orbit, which relies on the inverse square nature of gravitational force, thus failing under an inverse cube law.
Therefore, only the law of areas holds. Thus, the correct option is A.