There are some cases where the mass of an object does seem to depend on its volume. For example, if you fill a balloon with air, the balloon will become heavier. This is because the air inside the balloon has mass. However, the mass of the air is not actually dependent on the volume of the balloon. It is actually the density of the air that is changing. As the balloon is filled with air, the density of the air inside the balloon increases. This means that there is more mass per unit volume of air inside the balloon.
So, while it may seem like the mass of an object depends on its volume, it is actually the density of the object that is determining its mass.