Square Pattern Sequence: Finding the 64-Square Structure Position

To determine the sequence that forms these structures, observe the pattern that these are square grids building up: 1-by-1, 2-by-2, 3-by-3. This creates the series $1^2, 2^2, 3^2, \ldots, n^2$. We are asked to verify if 64 can be represented in this series.

Let's solve $n^2 = 64$ to find out which structure provides 64 squares:

• Start by taking the square root of both sides: $\sqrt{n^2} = \sqrt{64}$.
• This simplifies to $n = 8$, since $\sqrt{64} = 8$.

This confirms that the structure with 64 squares is indeed possible and corresponds to the 8th element in our series.

Therefore, the element of the series with 64 squares is $8$.