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Existing multiply robust estimators for causal mediation analysis assume independently distributed data, limiting their use in education research. In this study, we extend a multiply robust estimator to estimate causal mediation effects with a single mediator in clustered data, accommodating unmeasured cluster-level confounding. To reduce bias from model misspecification, we incorporate machine learning techniques for nuisance model estimation. The method accommodates binary and continuous mediators and outcomes, and targets both cluster-average and individual-average versions of the causal mediation effects. We evaluate the method's performance through simulation, and illustrate the method using data from the National Longitudinal Study of Adolescent to Adult Health (Add Health).