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Infinitely many.
Select any number A such that 0 < A ≤ cuberoot(24) = 2.8845 approx.
Then let S = 24/A
Next, let B be a number such that A ≤ B ≤ sqrt(S)
and let C = 24/(A*B)
Then it can be shown that A ≤ B ≤ C
and a cuboid with sides of length A, B and C will ave a volume of A*B*C = 24 cm3.
There are infinitely many possible values for A so that there are infinitely many possible cuboids.
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