  We present explicit expressions of the thermodynamic volume inside and
outside the cosmological horizon of Eguchi-Hanson solitons in general odd
dimensions. These quantities are calculable and well-defined regardless of
whether or not the regularity condition for the soliton is imposed. For the
inner case, we show that the reverse isoperimetric inequality is not satisfied
for general values of the soliton parameter $a$, though a narrow range exists
for which the inequality does hold. For the outer case, we find that the mass
$M_{out}$ satisfies the maximal mass conjecture and the volume is positive. We
also show that, by requiring $M_{out}$ to yield the mass of dS spacetime when
the soliton parameter vanishes, the associated cosmological volume is always
positive.
