Number of squares of size $1 = 10^2 = 100$
Number of squares of size $2 = 9^2 = 81$
Number of squares of size $3 = 8^2 = 64$
Number of squares of size $4 = 7^2 = 49$
Number of squares of size $5 = 6^2 = 36$
Number of squares of size $6 = 5^2 = 25$
Number of squares of size $7 = 4^2 = 16$
Number of squares of size $8 = 3^2 = 9$
Number of squares of size $9 = 2^2 = 4$
Number of squares of size $10 = 1^2 = 1$
Total number of squares $ =$ Sum of squares till $10$
$\qquad= \dfrac{n(n+1)(2n+1)}{6}$
$\qquad =\dfrac{10.11.21}{6}=385$