We construct higher-dimensional generalizations of the Eguchi-Hanson
gravitational instanton in the presence of higher-curvature deformations of
general relativity. These spaces are solutions to Einstein gravity supplemented
with the dimensional extension of the quadratic Chern-Gauss-Bonnet invariant in
arbitrary even dimension $D=2m\geq 4$, and they are constructed out of
non-trivial fibrations over $(2m-2)$-dimensional K\”ahler-Einstein manifolds.
Different aspects of these solutions are analyzed; among them, the
regularization of the on-shell Euclidean action by means of the addition of
topological invariants. We also consider higher-curvature corrections to the
gravity action that are cubic in the Riemann tensor and explicitly construct
Eguchi-Hanson type solutions for such.
