The conversion will vary with the drug. Milligram (mg) is a factor of concentration or strength (how much drug) while cubic centimeter (cc) aka milliliter (ml) is a factor of volume.
I sometimes use coffee as an illustration to help non-clinical staff with these concepts.
...For example, small, medium or large or tall, grande or venti describe the volume of the drink but not how strong it is.
Whereas "shots" describe the concentration or strength, i.e. 2 shots of espresso is not as strong as 4 shots of espresso.
So a tall cup of coffee with four shots of espresso is stronger than a tall cup of coffee with one shot. But a tall cup of coffee with no extra shots versus a venti cup of coffee with no extra shots have the same strength or concentration but just different volume.
So depending upon the HCPCS code description for the drug, you may need to know one or the other or both. For example, if 2 cc (volume) of Kenalog 40mg / cc (concentration / strength) is injected, the provider actually injected a total of 80 mg of Kenalog (40 * 2) and would be reported with 8 units of J3301.
Whereas if 1 cc of Kenalog 40 mg /cc were injected (less volume but same strength), only 40 mg was injected and 4 units of J3301 would be billed. We would bill the same units of J3301 for 4 cc of Kenalog 10 mg / cc (more volume of less concentrated)
So volume (cc, ml, liters, etc) is not synonomous with concentration / strength (micrograms, milligrams, grams, etc)