Triangular numbers and Oblong numbers

http://en.wikipedia.org/wiki/Triangular_number

http://en.wikipedia.org/wiki/Pronic_number

http://planetmath.org/encyclopedia/OblongNumber.html

1 + 2 + 3 + ... + n = n(n + 1)/2

And adding the successive odd numbers, we get

1 + 3 + 5 + ... + (2n - 1) = n^2

And if we sum the series of even numbers

2 + 4 + ... + 2n = n(n + 1)

8 * n(n + 1)/2 + 1 = 4n^2 + 4n + 1 = (2n + 1)^2

( 8 times any triangular number + 1 makes a square )

The difference between the squares of any two consecutive triangular numbers is always

a cube:
http://mathworld.wolfram.com/TriangularNumber.html


The oblong number is double of a triangular number.

The successive oblong numbers are:
2*3 = 6, 3*4 = 12, 4*5 = 20, ... n(n + 1), ...

When is the Product of Two Oblong Numbers Another Oblong?

http://www.jstor.org/pss/2691083

Question :

Show that Gauss's discovery that every number is the sum of three or fewer triangular numbers implies that every number of the form 8k + 3 can be expressed as the sum of three odd squares