Volume Comparison of Cube and Cylinder

A circular cylindrical container has a radius of 4 cm and a height of 10 cm. It is filled with a liquid. A cube with a side length of 6 cm is then submerged in the liquid. Determine whether the cube will fit inside the container when fully submerged, considering the volume of both the container and the cube. For this problem, use the formulas for the volume of a cylinder and the volume of a cube:

Volume of a cylinder: $$V = \pi r^2 h$$

Volume of a cube: $$V = s^3$$

Your task is to find the volume of both the container and the cube, then compare these volumes to conclude whether the cube will fully submerge without overflowing the liquid.