Mini-Challenge #5: Triangular square numbers

What is the smallest square triangular number whose triangular side is the square of a composite number?

Email the answer to pi3challenge@sheffield.ac.uk or tweet to @pi3challenge

Square numbers are those which can be arranged into a square as below, i.e., 1, 4, 9, 16, 25, etc.
Triangular numbers are those which can be arranged into a triangle as below, e.g., 1, 3, 6, 10, 15, 21, etc.

A square triangular number is a number which is both square and triangular. A composite number is one which can be factorized (in other words, a non-prime number greater than 1).