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A decimeter is ten times smaller than a meter
A cubic meters means one meter to the power of three. It is a measuring unit for volume and is equal to 1000 liters. When you have a cube with the side of one meter you have a cubic meter volume. Another name for a cubic meter is a stere
No, they were named after a town
A meter is a measure of length. So a measure that is 1000 times larger than a metre would still be a length: it would never ever be a volume. So the question makes no sense.
The distance which is 10^-3 larger is 1.003 metres, and there is no specific name for it. The name of the distance which is 10^-3 times as large (not the same thing!) is a millimetre.