Two men start a conversation by looking at a 5 digit number
1st Man : Its a perfect square
2nd Man: If I remove 2nd digit, it is still a perfect square
1st Man: If I remove 1st 2 digits, it is still a square!
2nd Man: Sum of the digits is equal to the first 2 digits
1st Man: If you add first two digits with the last 3 digits (AB + CDE), the resulting number is difference of a perfect cube - perfect square
2nd Man: If I remove the 2nd and 4th digit, the resulting number is a perfect cube
What's the number?
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