  We show a new example of blow-up behaviour for the prescribed $Q$-curvature
equation in even dimension $6$ and higher, namely given a sequence
$(V_k)\subset C^0(\mathbb{R}^{2n})$ suitably converging we construct {for
$n\geq 3$} a sequence $(u_k)$ of radially symmetric solutions to the equation
$${(-\Delta)^n u_k=V_k e^{2n u_k} \quad \text{in }\mathbb{R}^{2n},}$$ with
$u_k$ blowing up at the origin \emph{and} on a sphere. We also prove sharp
blow-up estimates. This is in sharp contrast with the $4$-dimensional case
studied by F. Robert (J. Diff. Eq. 2006).
