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Whilst I don't really like considering time as a spatial dimension, I would hazard that the answer will be the delightfully SI answer of 1 second.
The dimensions of the cube are 1x1x1, a unit for each dimension, so 1 metre by 1 metre by 1 second makes sense to me. This is of course assuming you measure time in increments of 1 second...
Also, if you were to plot this in 3D, using time as a 3rd spatial dimension, it should look like a cube, so it would have to be one unit in the time dimension.
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