  We derive the gravitational energy-momentum pseudo-tensor
$\tau^\mu_{\phantom{\mu}\nu}$ in both Palatini and metric approaches to $f(R)$
gravity. We then obtain the related cosmological gravitational energy density.
Considering a flat Friedmann-Lema\^itre-Robertson-Walker spacetime, the energy
density complex of matter and gravitation vanishes in the metric approach, but
results non-vanishing in the Palatini formalism. This feature could be relevant
in order to physically discriminate between the two approaches.
