let the 1st number be n^2
sum of 6 consecutive squares is
n^2+(n+1)^2+(n+2)^2+(n+3)^2+(n+4)^2 + (n+5)^2
= 6n^2+ 30n + 55
= 6n(n+5) + 55
1st part 6n(n+5)is divsible by 4 as either n or n+ 5 is even
so 6n(n+5) + 55 mod 4 = 55 mod 4 = 3
it cannot be a perfect square as perfect square mod 4 = 0 or 1
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