Introduction:
When a solid metallic cube is brought into contact with a reservoir at a different temperature, heat transfer occurs between them until they reach thermal equilibrium. In this process, the total entropy of the universe changes.

Explanation:
1. Initial state:
The metallic cube is at a temperature of 300K, and the reservoir is at a temperature of 600K. The cube and the reservoir are in thermal isolation from the surroundings.

2. Heat transfer:
When the cube is brought into contact with the reservoir, heat transfer occurs between them. The heat flows from the reservoir to the cube until they reach thermal equilibrium. The amount of heat transferred is given by the equation:
Q = m * c * ΔT
Where Q is the heat transferred, m is the mass of the cube, c is the specific heat capacity of the cube material, and ΔT is the change in temperature.

3. Entropy change of the cube:
The entropy change of the cube can be calculated using the equation:
ΔS_cube = Q / T_cube
Where ΔS_cube is the entropy change of the cube, Q is the heat transferred, and T_cube is the temperature of the cube.

4. Entropy change of the reservoir:
Similarly, the entropy change of the reservoir can be calculated using the equation:
ΔS_reservoir = Q / T_reservoir
Where ΔS_reservoir is the entropy change of the reservoir, Q is the heat transferred, and T_reservoir is the temperature of the reservoir.

5. Total entropy change of the universe:
The total entropy change of the universe is given by the sum of the entropy changes of the cube and the reservoir:
ΔS_universe = ΔS_cube + ΔS_reservoir

6. Final state:
After reaching thermal equilibrium, the cube and the reservoir will have the same temperature, T_final. The entropy change of the universe can be calculated using the equation:
ΔS_universe = Q / T_final

Conclusion:
In this process, heat transfer occurs between the cube and the reservoir until they reach thermal equilibrium. The entropy change of the universe is determined by the heat transferred and the final temperature. The entropy change of the cube and the reservoir can be calculated using their respective temperatures.