No, it is not.
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If by cube you mean perfect cube (a cube of an integer), then no, and the nearest perfect cube is 81.
It is a perfect cube.
It is not a perfect cube.
729, cube of 9 and square of 27
Perfect Square between roman numbers 100 to 300 are: 100, 121, 144, 169, 196, 225, 256, 289.