SMO 2005 Open Round 1 Question 16

Let $a_1=21$ and $a_2=90$, and for $n\ge3$, let $a_n$ be the last two digits of $a_{n-1}+a_{n-2}$. What is the remainder of $a_1^2+a_2^2+\cdots+a_{2005}^2$ when it is divided by $8$?