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Based on updated pulsation models for Classical Cepheids, computed forvarious assumptions about the metallicity and helium abundance, roughlyrepresentative of pulsators in the Small Magellanic Cloud ($Z$=$0.004$ and$Y$=$0.25$), Large Magellanic Cloud ($Z$=$0.008$ and $Y$=$0.25$), and M31($Z$=$0.03$ and $Y$=$0.28$), and self-consistent updated evolutionarypredictions, we derived Period-Age and multi-band Period-Age-Color relationsthat also take into account variations in the Mass-Luminosity relation. Theseresults, combined with those previously derived for Galactic Cepheids, wereused to investigate the metallicity effect when using these variables as ageindicators. In particular, we found that a variation in the metal abundanceaffects both the slope and the zero point of the above-mentioned relations. Thenew relations were applied to a sample of Gaia Early Data Release 3 ClassicalCepheids. The retrieved distribution of the individual ages confirms that abrighter Mass-Luminosity relation produces older ages and that First Overtonepulsators are found to be concentrated towards older ages with respect to theFundamental ones at a fixed Mass-Luminosity relation. Moreover, the inclusionof a metallicity term in the Period-Age and Period-Age-Color relations slightlymodifies the predicted ages. In particular, the age distribution of theselected sample of Galactic Cepheids is found to be shifted towards slightlyolder values, when the F-mode canonical relations are considered, with respectto the case at a fixed solar chemical composition. A marginally oppositedependence can be found in the noncanonical F-mode and canonical FO-mode cases.

Period-Age-Metallicity and Period-Age-Color-Metallicity relations for Classical Cepheids: an application to the Gaia EDR3 sample