The original volume is \(2\times3\times4=24\text{ cm}^3\).

Doubling only the first dimension gives \(4\times3\times4=48\text{ cm}^3\).

Doubling all three gives \(4\times6\times8=192\text{ cm}^3\).

The latter introduces three factors of two, giving multiplier \(2\times2\times2=8\).

Answer

Doubling one dimension gives \(48\text{ cm}^3\), twice the original. Doubling all dimensions gives \(192\text{ cm}^3\), eight times the original.