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Measurements of electroweak precision observables at future electron-positroncolliders, such as the CEPC, FCC-ee, and ILC, will be sensitive to physics atmulti-TeV scales. To achieve this sensitivity, precise predictions for theStandard Model expectations of these observables are needed, includingcorrections at the three- and four-loop level. In this article, results arepresented for the calculation of a subset of three-loop mixed electroweak-QCDcorrections, stemming from diagrams with a gluon exchange and two closedfermion loops. The numerical impact of these corrections is illustrated for anumber of applications: the prediction of the W-boson mass from the Fermiconstant, the effective weak mixing angle, and the partial and total widths ofthe Z boson. Two alternative renormalization schemes for the top-quark mass areconsidered, on-shell and $\overline{\mbox{MS}}$.

Mixed EW-QCD leading fermionic three-loop corrections at $\mathcal{O}(\alpha_s\alpha^2)$ to electroweak precision observables