Why does the blue box look blue? Is it always blue? Will it look blue even in the dark or under a red light?

The colours we see is because of light reflected. Green leaves absorbs other colours of light and reflect green light out of 7 colours. Hence we see leaves are green. Similarly blue box is due to reflection of blue colour while others  are absorbed in it.
No,  it will not be blue under dark and red light because in dark there is no light hence we cannot see it,  it will look black as seen by our eyes.
 

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it always blue

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it will luk blue cs it is blue! the box will change its shade of blue in dark light it will bcome dark blue and in red light a shade of purple! :_)

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