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: 
$(a_1 + a_2 + \dots + a_n) \mod 8 = [(a_1 \mod 8) + (a_2 \mod 8) + \dots + (a_n \mod 8)] \mod 8$
How may terms are there in the sequence? Take the $n^{th}$ term to be $2n - 1$.
