re: OH@Mae despite my love for lying on the internet, i'm an algebraic number theorist and would never lie about Diophantine equations!
specifically, the only integer solution to the equation y³ = x² + 2 is (x, y) = (±5, 3), so you have 25 (square), 26 (weirdo), 27 (cube) and that's the only time that happens. i wrote out a proof of this on my 26th birthday :D
correction: of course (-5, 3) also works here. but still the square is 25 so the claim about 26 is correct.
