Oh ... and further support for the answer being 36:

It is both the square of six and a triangular number, making it a square triangular number.

It is also the only triangular number (other than one) whose square root is also a triangular number.

It is also a circular number – a square number that ends with the same integer by itself (6×6=36). So it's a square, triangular, circular number.

It is the number of degrees in the interior angle of each tip of a regular pentagram.

It is number of possible outcomes (not summed) in the roll of two distinct dice.

It is the largest numeric base that some computer systems support because it exhausts the numerals, 0-9, and the letters, A-Z.

And finally ... the sum of the integers from 1 to 36 is 666.

OK. I'll get back in my box now.