The Year with Squares

Its simple. For every new figure you add 4. So, to know how many squares form Figure 2018 you multiply 4 by 2017 and add 1, because you start with one square, and get the answer - 8069.

Thhe $2018^{th}$ sequence is formed after adding 2017 such sequences to the first square. Also, each sequence is formed by adding four squares to the previous one. So, the $2018^{th}$ sequence contain :

$4 \times 2017 + 1 = 8068 + 1 = 8069$

Notice, there is pattern if we continue in the same logic, which is $(N-1)\times 4 +1\implies 2017\times 4+1= \boxed{8069}$ squares needed. ( $N$ represents the number of squares.)