  We study the polyharmonic problem $\Delta^m u = \pm e^u$ in ${\mathbb
R}^{2m}$, with $m \geq 2$. In particular, we prove that {\sl for any} $V > 0$,
there exist radial solutions of $\Delta^m u = -e^u$ such that $$\int_{{\mathbb
R}^{2m}} e^u dx = V.$$ It implies that for $m$ odd, given arbitrary volume $V >
0$, there exist conformal metrics $g$ on ${\mathbb R}^{2m}$ with positive
constant $Q$-curvature and vol$(g) =V$. This answers some open questions in
Martinazzi's work.
