We investigated the cosmology in a higher-curvature gravity where the dimensionality of spacetime gives rise to only quantitative difference, contrary to Einstein gravity. We found exponential type solutions for flat isotropic and homogeneous vacuum universe for the case in which the higher-curvature term in the Lagrangian density is quadratic in the scalar curvature, $xi R^2$. The solutions are classified according to the sign of the cosmological constant, $Lambda$, and the magnitude of $Lambdaxi$. For these solutions 3-dimensional space has a specific feature in that the solutions are independent of the higher curvature term. For the universe filled with perfect fluid, numerical solutions are investigated for various values of the parameter $xi$. Evolutions of the universes in different dimensionality of spacetime are compared.
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