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 fourtetraquark currents with J P = 0 + , and then we perform an analytic calculation up to dimension eight in the operator product expansion. We keep terms which are linear in the strange quark mass m s , and in the end we find two possible tetraquark states with masses (5.57±0.15) and (5.58±0.15) GeV. We find that their charmed-partner masses lie in (2.54± 0.13) and (2.55 ± 0.13) GeV, respectively, and are hence accessible in experiments like BESIII and Belle.