The "observable universe" is finite and has a volume of
So first of all, allow me to point out that it doesn't make much sense to say 'the whole universe'. What do you mean by that?
The correct way of saying it would be the "observable universe" since that is the extent of where we can get direct information about the universe.
Some people speculate that we could perhaps detect the presence of "other universes" (i.e. beyond our "observable universe") somehow by looking at the effects these other universes would have on our "observable" universe.
But again, this is mere speculation at this point, and no evidence exists that there are other universes beyond the one that is observable.
To answer the question, assuming that this "whole universe" thing meant the "observable universe", then, the observable universe IS FINITE, and its volume CAN be calculated whether the expansion rate is accelerating or not. We also assume that the observable universe is spherical. Then, the volume would just be obtained from the equation of the volume
Now, the observable universe has a radius of 13.7~13.8 billion light-years (this is really just the distance to the Cosmic Microwave Background, or CMB).
Thus, the volume is about:
HOWEVER, this volume is not the CURRENT size of the observable universe, but is basically the limit of what we can look at. This sphere where we do see the CMB has, since then, expanded (and that, with its accelerating expansion), and has kept becoming bigger for the past 13.7 billion years.
Current estimates of the CURRENT size of the observable universe (which is beyond observable anymore) would be 46.5 billion years in radius and so, its current volume would be about: