A perfect square refers to any number multiplied by itself.

##### (i) Square “Pyramids”

The following sets of square numbers can be arranged in pyramidal patterns.

##### (ii) Consecutive Odd Numbers

Square numbers can be written as a series of consecutive odd numbers.

1^{2 }= 1 = 1

2^{2 }= 4 = 1 + 3

3^{2 }= 9 = 1 + 3 + 5

4^{2 }= 16 = 1 + 3 + 5 + 7

5^{2 }= 25 = 1 + 3 + 5 + 7 + 9

6^{2 }= 36 = 1 + 3 + 5 + 7 + 9 + 11

7^{2 }= 49 = 1 + 3 + 5 + 7 + 9 + 11 + 13

8^{2 }= 64 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15

9^{2 }= 81 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17

##### (iii) Magic Perfect Square

Here is an extraordinary magic square made up entirely of perfect squares. Find its Magic Sums.

**Solution**

8515