The integer cubes with cubes less than 2000 are:
13 = 1
23 = 8
33 = 27
43 = 64
53 = 125
63 = 216
73 = 343
83 = 512
93 = 729
103 = 1000
113 = 1331
123 = 1728
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There are two single-digit numbers less than 10 which are cubes of whole numbers. These are 13 (one cubed = 1) and 23 (two cubed = 8).
The perfect squares that are less than 20 are 0, 1, 4, 9, and 16.
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Any number squared except 0 is a perfect square so it follows that prime numbers are less common than perfect squares.
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