Nobody knows the size of the universe, as only a portion of it is observable. If the universe happens to have an infinitely large size, then its mass could also be infinite.
It is only the mass of the observable universe that can be in the purview of scientific enquiry.
What is of interest to physicists is the density of matter in the universe, as it is important in determining the fate of the universe: whether it will collapse one day or whether it will continue expanding forever.
The density of matter in the universe can be estimated by various means such as by studying the fluctuations in the Cosmic Microwave Background, superclusters, Big Bang nucleosynthesis, etc.
According to these estimates, the density of matter in the universe is about 3 x 10^(-30) g/cc. By comparing with the density of atmospheric air of ~1.23 g/cc, it becomes clear that the density of space is very close to that of vacuum.
Again, this density includes the contribution of dark matter. The density of luminous matter that we see as stars and galaxies is only about one-tenth of the figure given above.
The size of the observable universe is ~ 14 billion light years.
Using the above value of density gives a mass of about 3 x 10^55 g, which is roughly 25 billion galaxies the size of the Milky Way.
No body knows what lies beyond the 25 billion galaxies and how it could impact the mass and density calculations.