Perfect Cube
Third power, triple-confirmed.
The cube of an integer, like 8, 729 or 970299. Including 0 and 1 — and that's nearly all there is: only 101 cubes in the whole range.
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Cubes are a full order of magnitude sparser than squares: the range holds 101 of them, 0³ through 100³, or 0.01%. The gap 3k²+3k+1 between consecutive cubes grows quadratically — rolling a cube is about ten times harder than rolling a square.
A number that is both a square and a cube must be a sixth power, and the range holds exactly 11: 0⁶ through 10⁶. These double-duty powers score on both fronts and are quiet high-rollers in infinite mode.
Trivia: 1729 is the famous taxicab number — the smallest number expressible as a sum of two cubes in two ways: 1³+12³ = 9³+10³. Ramanujan blurted this out from his sickbed, and 1729 has never been dull since.