Is the sum of positive numbers < 10^6 close to even square more or less than sum of numbers close to odd square ?

A number is near even square if it is closer to even square than odd square else if is close to odd square. 

Let us take the numbers from (2n)^2 upto (2n+2)^2-1 that is from even square to the number 1 less than next even squares  that is from (2n)^2 upto (2n+2)^2-1.

That is from 4n^2 to 4n^4 + 8n + 3

Average of numbers = (8n^2 + 8n+ 3)/2

Total number of numbers = (8n+4)

Sum of numbers = (4n+2)(8n^2+8n + 3) ..1

Nuw numbers near odd square (2n+1)^2 (or 4n^2 + 4n + 1) are from 4n^2+ 2n+1 to 4n^2 + 6n + 2

Average of numbers = 2

Number of numbers = 4n+ 2

So sum of numbers near odd square = (2n+1)( (8n^2+ 8n + 3) ..2

Which is ½ of sum of numbers

So sum of numbers near odd square = sum of numbers near even square

taking the ranges from 0 to 2^2-1, 2^2 to 4^2- 1 so on upto 998^2 to 1000^2-1 we can each odd sum is same as even sum and hence sum of close to odd square is same as sum of close to even square.