  The elastic scattering properties of three bosons at low energy enter the
many-body description of ultracold Bose gases via the three-body scattering
hypervolume $D$. We study this quantity for identical bosons that interact via
a pairwise finite-range potential. Our calculations cover the regime from
strongly repulsive potentials towards attractive potentials supporting multiple
two-body bound states and are consistent with the few existing predictions for
$D$. We present the first numerical confirmation of the universal predictions
for $D$ in the strongly interacting regime, where Efimov physics dominates, for
a local nonzero-range potential. Our findings highlight how $D$ is influenced
by three-body quasibound states with strong $d$-wave or $g$-wave
characteristics in the weakly interacting regime.
