Yes - there is an infinite number of such numbers. Just take the counting numbers (1,2,3,4, etc...) and put them to the power of 6 (i.e. multiply it by itself 6 times). The sequence of such numbers...
343 is the palindromic and cube number. 7*7*7=343 7 is being times three times by itself to get this palindromic and cube number. Also 1331 is a palindromic and cube number.11*11*11=133111 is being...