Is there a centered-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?