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2 Corrected terminology: "centered hexagonal number" instead of "hexagonal number"

Is there a hexagonal, triangular, square (apart from 0 and 1)?
In other words, is there a positive integer that is simultaneously

(1) a perfect square, $n^2$, $n \ge 2$,

(2) a triangular number, $\frac{m(m+1)}{2}$, $m$ an integer,

and (3) a (centered) hexagonal number, $(p+1)^3 - p^3$, $p$ an integer?

1

# Hexagonal Triangular Squares

Is there a hexagonal, triangular, square (apart from 0 and 1)?
In other words, is there a positive integer that is simultaneously

(1) a perfect square, $n^2$, $n \ge 2$,

(2) a triangular number, $\frac{m(m+1)}{2}$, $m$ an integer,

and (3) a hexagonal number, $(p+1)^3 - p^3$, $p$ an integer?