How many squares?

No. of $1 × 1$ squares = ${10}^2$
No. of $2 × 2$ squares = ${9}^2$
No. of $3 × 3$ squares = ${8}^2$
No. of $4 × 4$ squares = ${7}^2$
No. of $5 × 5$ squares = ${6}^2$
No. of $6 × 6$ squares = ${5}^2$
No. of $7 × 7$ squares = ${4}^2$
No. of $8 × 8$ squares = ${3}^2$
No. of $9 × 9$ squares = ${2}^2$
No. of $10 × 10$ squares = ${1}^2$

So, the answet is $\displaystyle \sum_{n = 1}^{10} n^2 = \boxed{385}$ .