  In general relativity, the local gravitational energy is best characterised
by the quasilocal mass. The small sphere limit of quasilocal mass provides us
the most local notion of gravitational energy. In four dimensions, the limits
were shown be the stress tensor in non-vacuum and the Bel-Robinson tensor in
vacuum. We study the local gravitational energy in higher dimensions through
the lens of the small sphere limits of various quasilocal mass proposals which
can be appropriately generalised beyond four dimensions, and report a new
quantity $\Q$ which potentially characterises the local gravitational energy
content in vacuum. We find that the limits at presence of matter yield the
stress tensor as expected, but the vacuum limits are not proportional to the
Bel-Robinson superenergy $Q$ in dimensions $n>4$. The result defies the role of
the Bel-Robinson superenergy as characterising the gravitational energy in
higher dimensions, albeit the fact that it uniquely generalises. More
surprisingly, $\Q$ replace the Bel-Robinson superenergy $Q$ in all three
quasilocal mass proposals that we study. However, $\Q$ cannot be directly
interpreted as a local gravitational energy because of its non-positivity. The
physical meaning of $\Q$ awaits more evidence from investigating other
quasilocal masses in higher dimensions.
