You have your basic 3-4-5, 5-12-13, and 8-15-17 Pythagorean Triples which are just patterns that have been discovered by mathematicians along the ages, but here is a Wikipedia link if you want more depth: http://en.wikipedia.org/wiki/Formulas_for_generating_Pythagorean_triples
Also, here is a good link for a list of a lot of triples, plus cool graphics:
http://en.wikipedia.org/wiki/Pythagorean_triple
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There are infinitely many Pythagorean triples. To find a Pythagorean triple take two positive integers x, y with x > y. A Pythagorean triple is of the form x2 - y2, 2xy, x2 + y2.
You can use pythagorean theorem twice to find the diagonal of a cube
That will depend on the triples of which none have been given but in order to be a Pythagorean triple they must comply with Pythagoras' theorem for a right angle triangle.
Pythagorean theorem
C2=A2+B2 Therefore to find B2: B2=C2-A2