In this work we update the bounds on ∑ mν from latest publicly available cosmological data and likelihoods using Bayesian analysis, while explicitly considering particular neutrino mass hierarchies. In the minimal ΛCDM + ∑ mν model with most recent CMB data from Planck 2018 TT,TE,EE, lowE, and lensing; and BAO data from BOSS DR12, MGS, and 6dFGS, we find that at 95% C.L. the bounds are: ∑ mν<0.12 eV (degenerate), ∑ mν<0.15 eV (normal), ∑ mν<0.17 eV (inverted). The bounds vary across the different mass orderings due to different priors on ∑ mν. Also, we find that the normal hierarchy is very mildly preferred relative to the inverted, using both minimum χ2 values and Bayesian Evidence ratios. In this paper we also provide bounds on ∑ mν considering different hierarchies in various extended cosmological models: ΛCDM + ∑ mν+r, wCDM+∑ mν, w0 wa CDM+∑ mν, w0 wa CDM+∑ mν with w(z)-1, Λ CDM + ∑ mν + Ωk, and Λ CDM + ∑ mν + ALens. We do not find any strong evidence of normal hierarchy over inverted hierarchy in the extended models either.