Given that these are single atoms, why should the specific heat difference be so great? And more specifically, why does it take 36 times as much energy to raise the temperature of a given mass of Helium compared to Xenon?
The key question is "Per mole or per gram?" Because the both values can be found tabulated as "specific heat" in various sources. Perhaps it would be useful to distinguish "molar specific heat" from "specific heat per unit mass".
You seem to be using the intuition for the molar quantity, so if the table is by mass, the answer is simply that you need more moles of helium.