A cubefree number is a positive integer whose prime factorization has no exponent
greater than 2, so no cubic number greater than 1
divides it. All primes are therefore trivially cubefree.
The cubefree numbers are 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, ...
(OEIS A004709). The cubeful numbers (i.e.,
those divisible by a cubic number greater than 1)
are 8, 16, 24, 27, 32, 40, 48, 54, ... (OEIS A046099).
The numbers of cubefree numbers not exceeding 10, 100, 1000, ... are 9, 85, 833,
8319, 83190, 831910, ..., and their natural density
is 
, where 
is the Riemann
zeta function.
