AMC 10 2021-fall-a Problem 3

What is the maximum number of balls of clay of radius $2$ that can completely fit inside a cube of side length $6$ assuming the balls can be reshaped but not compressed before they are packed in the cube? $\textbf{(A) }3 \textbf{(B) }4 \textbf{(C) }5 \textbf{(D) }6 \textbf{(E) }7$