What are the largest known palindromic squares with a non-palindromic base, palindromic cubes with a...

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Problem

What are the largest known palindromic squares with a non-palindromic
base, palindromic cubes with a non-palindromic base, palindromic
triangular numbers and palindromic tetrahedral numbers?

[ Editor: problem statement reconstructed from the posting, a request
  for larger records. ]

Show solution

I'm always looking for all sorts of information about palindromic
numbers.  I devoted a whole website to these fascinating and beautiful
numbers.  Palindromic numbers are numbers that read the same from 'left
to right' as from 'right to left'.  Actually, my attention focuses
almost entirely on finding the next larger palindromic number.  That
number can be for instance a square, a triangular, a tetrahedral, a
cube, a pentagonal etc.  Here's a list of what I achieved so far:

Record_nr(?) for palindromic squares with NONpalindromic base
(sometimes called 'root')

        ( 306.950.094.269.977.057 ) ^ 2 =
        94.218.360.372.347.802.120.874.327.306.381.249 [length 35]

Record_nr(?) for palindromic cubes with NONpalindromic base

        ( 2.201 ) ^ 3 =
        10.662.526.601 [length 11]

Record_nr(?) for palindromic triangulars.  Function = (b*b+b)/2
                (Note that the base is also palindromic !)

        Function( 3.654.345.456.545.434.563 ) =
        6.677.120.357.887.130.286.820.317.887.530.217.766 [length 37]

Record_nr(?) for palindromic tetrahedrals; Function = (b*(b+1)*(b+2))/6

        Function( 336 ) =
        6.378.736 [length 7]

If you happen to know of similar basenumbers that are larger than the
ones above, please let me know your source.

-- Patrick De Geest <Patrick.DeGeest@ping.be>, January 1997
   URL : http://www.ping.be/~ping6758/index.html

[ Editor: the dots are thousands separators. ]