Buoyancy in gases:

According to the Archimedean Principle a body within a gas is affected by buoyancy. This buoyancy equals the weight force of the displaced gas:

The weight force is the product of mass and the gravitational constant:

You already know the mass. It is the product of density and volume:

Thereby is the density of the displaced gas.
is the volume of the body, which is within the gas.

Thus the Archimedean Principle also applies wihtin gases. A body within a gas is affected by buoyancy.
But if you fill a balloon with air, it will sink.
Its buoyancy is smaller than the weight force of the air and the balloon envelope: