The volume of a cube of ice for an ice sculpture is 64,000 cubic inches.
a. what is the edge length of the cube of ice?

edge length is 40 inches.

The edge length of a cube has the same measurement. 
Volume of a cube is computed by multiplying the edge length to itself twice.

Volume = edge length x edge length x edge length

If the given data is volume of the cube and edge length is required. simply find the cube root of the volume.

edge length = ∛volume
edge length = ∛64000 in³
edge length = 40 inches.

To check:
40 x 40 = 1600 x 40 = 64000