A search for Kaluza-Klein excited vector boson resonances, WKK, decaying in cascade to three W bosons via a scalar radion R, WKK→WR→WWW, in a final state containing two or three massive jets is presented. The search is performed with s=13 TeV proton-proton collision data collected by the CMS experiment at the CERN LHC during 2016-2018, corresponding to an integrated luminosity of 138 fb-1. Two final states are simultaneously probed, one where the two W bosons produced by the R decay are reconstructed as separate, large-radius, massive jets, and one where they are merged into a single large-radius jet. The observed data are in agreement with the standard model expectations. Limits are set on the product of the WKK resonance cross section and branching fraction to three W bosons in an extended warped extra-dimensional model and are the first of their kind at the LHC.