I would like to know, well from your calculations with a computer and your explanation of your computational method, or well with a theoretical argument how to show that an even perfect number, for example $8128$, is the sum of three palindromes.
The motivation is [1] and next paragraph, currently you can read the required justification of my question from the main theorem of [1] from arXiv (currently I don't know what is the journal editing this article).
From [1] you know what base can use, but if it is possible I would like to know the calculations in base $10$ (but if your base is different feel free to add your answer with such). I add as remark that is well known a representation in basis $2$ for each even perfect number (but we can't use the base $2$), see this Wikipedia.
Question. How do you write the even perfect number $8218$ as a sum of three palindromes for a suitable base? Many thanks.
If your calculations were with a computer, please explain, if it is possible, your method also with a different even perfect numbers, for example $33550336$.
Updated. The question was updated, now I am asking about $8128$ instead $496$.
References:
[1] Lewis Baxter, Javier Cilleruelo and Florian Luca, Every positive integer is a sum of three palindromes (2016). Available from arXiv as arXiv:1602.06208v2.
I think $8128$ is still too small to require an idea beyond guess-and-check. For example, we quickly see that $$8128 = 8118 + 9 + 1.$$
Even $33550336$ is a bit too small. Some trial and error led to $$33550336 = 33544533 + 4884 + 919.$$