You want the mass of one marble? There is not enough information to determine absolutely conclusively the mass of one marble. However, you can get a number that is very likely the mass of one marble, but in the unlucky case it could be an integer multiple of the mass. Also, I'm assuming the measurements are extremely accurate (i.e. you did not round up significant digits).

The idea is similar to that of Millikan's oil-drop experiment to determine the charge of a single electron.

To make things simple, lets get rid of decimal points and work in units of cg.

I.e. the masses are 3603g, 3041cg, 2493cg, ...

All of these numbers must be an integer multiple of the mass. This means that an integer multiple of the mass is the greatest common divisor of these numbers.

What is the greatest common divisor for 3603, 3041, 2493, ...? I get 1 because 3602 and 3041 are already relatively prime.

So the greatest common factor is 1cg=0.01g

This means that the mass m = (0.01 g)/(some integer). It is likely that "some integer" is 1 since you have many samples.

Why can't we know the exact mass? If we said m = 0.01 g, then we can also create an indistinguishable situation where m=0.001g and put 10 times as many marbles in each box to get the same masses.