Question

did you know that the difference between the squares of two consecutive numbers is always odd? Verify it with three consecutive 3-digit numbers

Answer 1

square of an even number gives an even number while square of an odd number gives an odd number. And we all know addition of an odd and even number gives an odd number ..
For eg. I will pick 2 and 3 as my numbers. 2^2+3^2=4+9=13

three consecutive integers example:-
will pick 5,6 &7 as my numbers.
5^2+6^2+7^2=25+36+49=110
Thus it is not true in the case of three consecutive integers

Answer 2

² of An Even number gives an even number while square of an odd number gives an odd number. 

For example we will take 2 and 3 as our numbers. 2² + 3² = 4 + 9 = 13.

Three consecutive integers examples are 
will pick 5,6 &7 as our numbers.
5² + 6² + 7² = 25 + 36 + 49 = 110.
∴ It is not true in the case of three consecutive integers.