You are correct that the two answers may seem similar at first, but there is actually a key difference between them. The best way to measure a 10 cm cube portion of a solution is to use option a: weigh 10 times the mass of a 1 cm cube of the solution.
The reason for this is that the density of a solution may not be exactly 1 g/cm³. Therefore, weighing 10 g (option b) may not necessarily give you a 10 cm³ volume of the solution. However, if you know the mass of 1 cm³ of the solution, multiplying it by 10 will give you the correct mass for a 10 cm³ volume.
However, if the solution is pure water, which has a density very close to 1 g/cm³, then both options would give you the correct measurement. This is because in the case of pure water, 10 g would indeed be very close to a 10 cm³ volume.