We study conformal metrics g u = e 2u |dx| 2 on R 2m with constant Q-curvature Q gu ≡ (2m − 1)! (notice that (2m − 1)! is the Q-curvature of S 2m ) and finite volume. When m = 3 we show that there exists V * such that for any V ∈ [V * , ∞) there is a conformal metric g u = e 2u |dx| 2 on R 6 with Q gu ≡ 5! and vol(g u ) = V . This is in sharp contrast with the fourdimensional case, treated by C-S. Lin. We also prove that when m is odd and greater than 1, there is a constant V m > vol(S 2m ) such that for every V ∈ (0, V m ] there is a conformal metric g u = e 2u |dx| 2 on R 2m with Q gu ≡ (2m − 1)!, vol(g) = V . This extends a result of A. Chang and W-X. Chen. When m is even we prove a similar result for conformal metrics of negative Q-curvature.