Is 2201 really the only non-palindromic number whose cube is palindromic?

Question

Hі,

Wikipedia states that 2201 is the "only known non-palindromic number whose cube is palindromic", and lists no reference. It is in fact true that $2201^3=10662526601$, which is a palindrome. But to say there isn't any other number with this property seems a rather bold statement. Is this provable?

Thanks,

Answer 1

A short computer run will verify this is true for all $n$ smaller than (updated) $10^{11}$.

import math,sys

def isPali(n): return str(n)[::-1] == str(n)
n = 0 
try:    
  while True:       
  n += 1        
  if not isPali(n) and isPali(n*n*n): print 'Found one!',n, n*n*n 
except KeyboardInterrupt:
  print 'Searched until', n 
  sys.exit()

Anyone with more computing time is welcome to add some powers to that $10$.