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There is no equivalence.
A microgram is a measure of mass. A cubic centimetre 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.
If you are not convinced, consider a cubic centimetre of air. How many micrograms? Next consider a cubic centimetre of lead. How many micrograms?
The masses of equal volumes of the two substances will clearly be very different. So there is no direct conversion between mass and volume: you need to know the density of the substance to enable you to carry out the conversion.
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