To what accuracy and precision do we know the volume of the Earth?
One way to approach this is to treat the Earth as an oblate ellipsoid. This would mean the errors arise from the uncertainties in the Earth's equatorial radius and the flattening. From Groten, "Fundamental Parameters and Current (2004) Best Estimates of the Parameters of Common Relevance to Astronomy, Geodesy, and Geodynamics," Journal of Geodesy 77:10-11, 724-797 (2004), the Earth's equatorial radius in the mean tide system is 6378136.72±0.10 meters, and the inverse flattening is 1/f = 298.25231±0.00001. The uncertainty in volume due to the uncertainty in equatorial radius is about $3 V \frac{\Delta a}{a}$, where $V=\frac 4 3 \pi (1-f) a^3$, or about 51,000 cubic kilometers. The uncertainty in volume due to the uncertainty in inverse flattening is tiny in comparison, about $V \frac {\Delta 1/f} {1/f (1/f - 1)}$, or about 120 cubic kilometers.

That 51,000 cubic kilometer figure sounds like a lot, but it's not. It means the volume of the Earth can be expressed to seven places of precision.