Jimmy is filling a rectangular box with sugar cubes. If the dimensions of the box are $12$" by $16$" by $12$" and the sugar cubes have side length of $4$", then how many sugar cubes can fit in the box?

A. $12$

B. $144$

C. $36$

D. $48$

E. $576$

A. $12$

B. $144$

C. $36$

D. $48$

E. $576$