  In this work, we estimate the masses of tetraquark states with four different
flavors by virtue of QCD sum rules, in both $b$ and $c$ sectors. We construct
four $[8_c]_{\bar{b} s} \otimes [8_c]_{\bar{d} u}$ tetraquark currents with
$J^P = 0^+$, and then perform analytic calculation up to dimension eight in the
Operator Product Expansion (OPE). We keep terms which are linear in the strange
quark mass $m_s$, and in the end find two possible tetraquark states with
masses $(5.57 \pm 0.15)$ and $(5.58 \pm 0.15)$ GeV. We find that their
charmed-partner masses lie in $(2.54 \pm 0.13)$ and $(2.55 \pm 0.13)$ GeV,
respectively and are hence accessible in experiments like BESIII and Belle.
