  We have probed a cosmological model in $f(R)$-gravity, which is a cubic
equation in scalar curvature $R$. The terms arise due to nonlinear $f(R)$
function are treated as energy due to curvature inspired geometry. As a result,
we find accelerating expansion in the universe, which creates an
anti-gravitating negative pressure in it. Some of the physical parameters are
solved using numerical methods. The evolution of the model are examined by the
latest observational Hubble data (46-data points) and Pantheon data (the latest
compilation of SNIa with 40 binned in the redshift range $0.014 \leqslant z
\leqslant1.62$). Some important features of the model have been discussed by
analyzing the plots of various dynamical parameters. The plots of deceleration
parameter $q$ and the Hubble parameter $H$ describe the accelerating expansion
in the evolution of the Universe at the present epoch. The transition from
deceleration to acceleration for our model is obtained at redshift $z_{tr}
\simeq 0.694069$, which is in good agreement with $\Lambda$CDM. We have also
carried out state finder analysis for our model. The analysis of specific
features of the model confirms that our model is consistent with $\Lambda$CDM
in late times.
