Mass quantifies the amount of body matter an object has. Unless you change the amount of matter in said object, it's mass will always remain constant, regardless of which planet it's on.
What would change on different planets is weight. This is a perceived quantity, which quantifies the amount of force exerted on the object by gravity. Weight is typically quantified as
This is a subtle but key distinction that you must be able to make when in the field of physics.
If you're interested, this video by Khan Academy goes into this topic at length:
Hope that helped :)