A body that has a a mass of 80 kg on earth will also have a mass of 80 kg on the moon or anywhere else. Mass is the amount of matter something contains, so it doesn't vary with location.
What does vary with location is weight. Weight is the force exerted by mass due to gravity. Acceleration due to gravity on the moon is 1.6 m/s^2 and on Earth it's 9.8 m/s^2. An object on the moon weighs about 1/6 what it weighs on earth because of this difference. Weight = mass x accelertion due to gravity, or F=ma.
The difference in gravitational attraction is due to the different masses of the moon and Earth. Gravitional attraction is proportional to the product of the two masses being attracted, which in this case is the 80 kg object being attracted to either the moon or Earth.