Curious Calculations

Perfect Square that are Palindromes:

121=11²
484=22²
676=26²
10201=101²
12321=111²
14641=121²
40804=202²
44944=212²

Perfect Cubes that are Palindromes

343=7³
1331=11³
1030301=101³
1367631=111³
 
 
All palindromic primes with 3 digits:

101
131
151
181
191
313
353
373

Pick a number. Add the number, which you must read from the right to the left (mirror number), to the original number. Maybe the sum is a palindrome. If the sum isn't a palindrome, add the mirror number of the sum to the sum. Maybe you have a palindrome now, otherwise repeat the process. Nearly all numbers have a palindrome in the end.
Example: 49 49+94=143 143+341= 484 !
There are some numbers, which have no palindromes. The lowest one is 196. But the proof is still missing.

Interesting Pair of Squares

12² = 144 and 21² = 441
13² = 169 and 31² = 961
102²=10404 and 201²=40401
103²=10609 and 301²=90601
112²=12544 and 211²=44521
113²=12769 and 311²=96721
1012²=1024144 and 2101²=4414201
1112²=1236544 and 2111²=4456321
1212²=1468944 and 2121²=4498641
2012²=4048144 and 2102²=4418404

69696=264²
94249=307²
698896=836²
1002001=1001²
1234321=1111²
4008004=2002²
5221225=2285².