It depends on the substance being measured. If it's water, 1g = 1ml so 125g = 125ml.
The best way to get round it would be to place your measuring jug on your scales, adjust them so they read 0g while the jug is in place and then pour whatever it is you're trying to measure into the jog until 125g of it is reached.
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No.
A millilitre (ml) is a measure of volume, with dimensions [L3]. A gram is a measure of mass, with dimensions [M]. Basic dimensional analysis teaches that you cannot convert between measures with different dimensions such as these without additional information. It takes only a little mental effort to compare a gram of air and a gram of lead and come to the conclusion that the two will have very different volumes.