A number AABCBC is the square of an integer. Find all possible values of AABCBC.

(In reply to

More than expected by Jer)

Jer:

I agree with the 3.3% probability of having 3 or more solutions, but that does not mean that there is something more going on here. 1 in 30 chances occur all the time. If you roll a pair of dice and they come up snake eyes, would you conclude that they are unfair dice, just because the probability of snake eyes is 1/36? I think that 3 squares that fit the pattern is well within the realm of possibility.