No odd ones are divisible by 8
So we have
8^2 = 64 = 8 * 8
12^2 = 144 = 8 * 18
16^2 = 256 = 8 * 32
20^2 = 400 = 8 * 50
24^2 = 576 = 8 * 72
28^2 = 784 = 8 * 96
What about 16?
I believe there are 7 because \(\lfloor\sqrt{1000}\rfloor=31~\text{and}~\lfloor\frac{31}{4}\rfloor=7\)