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We investigate possible regimes in spatially flat vacuum cosmological modelsin cubic Lovelock gravity. The spatial section is a product of three- andextra-dimensional isotropic subspaces. This is the second paper of the seriesand we consider D=5 and general D>=6 cases here. For each D case we foundcritical values for $\alpha$ (Gauss-Bonnet coupling) and $\beta$ (cubicLovelock coupling) which separate different dynamical cases and study thedynamics in each region to find all regimes for all initial conditions and forarbitrary values of $\alpha$ and $\beta$. The results suggest that for D>=3there are regimes with realistic compactification originating from `generalizedTaub' solution. The endpoint of the compactification regimes is eitheranisotropic exponential solution (for $\alpha > 0$, $\mu \equiv \beta/\alpha^2< \mu_1$ (including entire $\beta < 0$)) or standard Kasner regime (for $\alpha> 0$, $\mu > \mu_1$). For D>=8 there is additional regime which originates fromhigh-energy (cubic Lovelock) Kasner regime and ends as anisotropic exponentialsolution. It exists in two domains: $\alpha > 0$, $\beta < 0$, $\mu \leqslant\mu_4$ and entire $\alpha > 0$, $\beta > 0$. Let us note that for D>=8 and$\alpha > 0$, $\beta < 0$, $\mu < \mu_4$ there are two realisticcompactification regimes which exist at the same time and have two differentanisotropic exponential solutions as a future asymptotes. For D>=8 and $\alpha> 0$, $\beta > 0$, $\mu < \mu_2$ there are two realistic compactificationregimes but they lead to the same anisotropic exponential solution. Thisbehavior is quite different from the Einstein-Gauss-Bonnet case. There are twomore unexpected observations among the results -- all realisticcompactification regimes exist only for $\alpha > 0$ and there is no smoothtransition from high-energy Kasner regime to low-energy one with realisticcompactification.

Realistic compactification in spatially flat vacuum cosmological models in cubic Lovelock gravity: High-dimensional case