1*mL1⋅mL == 1*cm^31⋅cm3, are we agreed on this?
But 1*cm^31⋅cm3 == (1xx10^-2*m)^3(1×10−2⋅m)3, because the "centi prefix"centi prefix -=≡ 10^-210−2.
And thus (1xx10^-2*m)^3(1×10−2⋅m)3 == 1xx10^-2*mxx1xx10^-2*mxx1xx10^-2*m=1×10−2⋅m×1×10−2⋅m×1×10−2⋅m=
1xx10^-6*m^31×10−6⋅m3
And so finally, (1*mL)/(1*m^3)=(1xx10^-6*m^3)/(1*m^3)=10^-61⋅mL1⋅m3=1×10−6⋅m31⋅m3=10−6.
Alternatively (finally again) (1*m^3)/(1*mL)=(1*m^3)/(1xx10^-6*m^3)=10^(+6)1⋅m31⋅mL=1⋅m31×10−6⋅m3=10+6.
Thus there are 10^6106, "one million"one million, mLmL in a "cubic meter"cubic meter.
We use the same methodology to show that there are 1000*L1000⋅L in a "cubic meter"cubic meter. A m^3m3 is a VERY large volume.
