  We identify time-reversal symmetry breaking mixed-parity superconducting
states that feature eight Majorana corner modes in properly cleaved
three-dimensional cubic crystals. Namely, when an odd-parity isotropic $p$-wave
pairing coexists with cubic symmetry preserving even-parity octupolar
$d_{x^2-y^2}+i d_{3z^2-r^2}$ pairing, the gapless surface Majorana modes of the
former get localized at the eight corners, thus yielding an \emph{intrinsic}
third-order topological superconductor (TOTSC). A cousin $d_{xy}+id_{3z^2-r^2}$
pairing also accommodating eight corner Majorana modes, by virtue of breaking
the cubic symmetry, in contrast, yields an \emph{extrinsic} TOTSC. We identify
a doped octupolar (topological or trivial) Dirac insulator as a suitable
platform to sustain such unconventional superconductors, realized from an
intraunit cell pairing. Finally, we argue that the proposed TOTSC can be
experimentally realizable in NaCl and other structurally similar compounds
under high pressure.
