It is conventionally argued that dark matter (DM) has a non-baryonic nature, but if we assume that DM was frozen out before primordial nucleosynthesis and could not significantly impact primordial abundances this argument may be evaded. Then a hypothetical SU(3) flavor-singlet, highly symmetric, deeply bound neutral scalar hexaquark S = uuddss, which due to its features has escaped from experimental detection so far, may be considered as a candidate for a baryonicDM. In the presentwork we calculate themass and coupling constant of the scalar six-quark particle S by means of the QCD sum rule method. Our predictions for its mass are m(S) = 1180(-26)(+40) MeV (m(s) = 95 MeV) and (m) over tilde (S) = 1239(-28)(+42) MeV (m(s) = 128 MeV). Although these values of mass would produce thermally the cosmologicalDMabundance, existence of this state may contradict the stability of the oxygen nuclei, which requires further thorough analysis.