Junior Mathematical Olympiad 2008 Section B Q16

[JMO 2008 B1 Edited] Tamsin has a selection of cubical boxes whose internal dimensions are whole numbers of centimetres, that is, 1cm $\times$ 1cm $\times$ 1cm, 2cm $\times$ 2cm $\times$ 2cm, and so on. What is the side length of the smallest of these boxes in which Tamsin could fit ten rectangular blocks each measuring 3cm $\times$ 2cm $\times$ 1cm without the blocks extending outside the box?