 Squared triangular number

A squared triangular number is the square of a number $T_n$, where $T_n$ is a triangular number. Beginning at $n=0$, the values are $0,1,9,36,100,225,441,\dots$. Nicomachus's theorem gives them a second description as cumulative sums of cubes of numbers.

A squared triangular number is a special type of number that is both a triangular number and a perfect square. A triangular number is a number that can form an equilateral triangle. The \( n \)-th triangular number is given by the formula: \[ T_n = \frac{n(n + 1)}{2} \] A perfect square is an integer that is the square of an integer.