There can be no conversion.
A ton is a measure of mass. A cubic metre is a measure of volume. The two measure different things and, according to basic principles of dimensional analysis, conversion from one to the other is not valid.
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There is no such thing as a "cubic ton". There is the ton as a unit of mass (1 ton = 1000 kg), and there is the cubic meter, a unit of volume.
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Dust or solid?
There is no general conversion, since a ton is a measure of mass, and a cubic meter is a unit of volume. It depends on the density of the substance you are talking about.