  We construct a plethora of new Euclidean AdS-Taub-NUT and bolt solutions of
several four- and six-dimensional higher-curvature theories of gravity with
various base spaces $\mathcal{B}$. In $D=4$, we consider Einsteinian cubic
gravity, for which we construct solutions with
$\mathcal{B}=\mathbb{S}^2,\mathbb{T}^2$. These represent the first
generalizations of the Einstein gravity Taub-NUT/bolt solutions for any
higher-curvature theory in four dimensions. In $D=6$, we show that no new
solutions are allowed for any Generalized quasi-topological gravity at cubic
order. They exist however when we consider quartic Quasi-topological and
Generalized quasi-topological terms, for which we construct new solutions with
$\mathcal{B}=\mathbb{CP}^2,\mathbb{S}^2\times\mathbb{S}^2,\mathbb{S}^2\times\mathbb{T}^2,\mathbb{T}^2\times\mathbb{T}^2$.
In all cases, the solutions are characterized by a single metric function, and
they reduce to the corresponding ones in Einstein gravity when the
higher-curvature couplings are set to zero. While the explicit profiles must be
constructed numerically (except for a few cases), we obtain fully analytic
expressions for the thermodynamic properties of all solutions. The new
solutions present important differences with respect to Einstein gravity,
including regular bolts for arbitrary values of the NUT charge, critical
points, and re-entrant phase transitions.
