Absolutely right, TPHacker! . . . *blush*

Everybody, please ignore this egregious incorrect solution . . .

The cubes are: n³

The triangular numbers are: n(n + 1)/2

Then we have: n³ = n(n+1)/2 ---> 2n³ - n² - n = 0

Factor: n(n - 1)(2n + 1) = 0

Sincenis a positive integer, the only root is: n = 1