The remainder of $1^2+3^2+5^2+7^2+\cdots+1013^2$ divided by $8$ How to find the remainder of $1^2+3^2+5^2+7^2+\cdots+1013^2$ divided by $8$

Hint:  calculate the remainder each of the first few terms contributes.  You should be able to make a reasonable hypothesis, then confirm it.  What is the remainder when $(2k+1)^2$ is divided by $8?$  How many terms are in the sum?
