A large plastic storage bin has dimensions of \(16 \mathrm{~cm} \times 16 \mathrm{~cm} \times 16 \mathrm{~cm}\). A medium bin's dimensions are half the size of the large bin. A small bin's dimensions are the size of the medium bin. If the storage bins come in a set of 3-small, medium, and large-what is the total volume of the storage bin set in cubic centimeters?