What is the volume of the universe?

Based on your comments, I think your confusion comes from having seen the classic rugby ball-shaped image of the CMB.
The CMB we observe is not from the whole cosmos, but only from a thin and completely spherical shell centered on us, with a radius $R_mathrm{CMB}simeq45.6,mathrm{Gly}$ (using a Planck 2015 cosmology). Just as the shell of Earth can be projected onto a rugby-shaped figure using a Mollweide projection, so can the shell of the CMB. Here's a figure from Universe Adventure that can help visualize:

Although we (still) can't see beyond the CMB, the observable Universe is all the way out to redshift $z=infty$, while the CMB comes from $zsimeq1100$, but the difference is not big; $R_mathrm{obs.Uni.} simeq 47,mathrm{Gly}$. Thus, the volume of the observable Universe is

$$V = frac{4pi}{3}R_mathrm{obs.Uni.}^3 = 435,!000,mathrm{Gly}^3.$$

The total Universe is probably much, much larger, and may in fact easily be infinite.

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