To determine if it is possible to build a $4 \times 4 \times 4$ cube from blocks consisting of 4 unit cubes, we need to consider the following:

1. Volume Calculation:
- The volume of the $4 \times 4 \times 4$ cube is:
$$4 \times 4 \times 4 = 64 \text{ unit cubes}$$
- Each block consists of 4 unit cubes. Therefore, the number of such blocks needed to fill the $4 \times 4 \times 4$ cube is:
$$\frac{64}{4} = 16 \text{ blocks}$$

2. Shape and Tiling:
- We need to ensure that the blocks can be arranged to completely fill the $4 \times 4 \times 4$ cube without any gaps or overlaps.
- The problem does not specify the exact shape of the blocks, but we can assume they are tetrominoes (shapes made of 4 unit cubes).

3. Parity Consideration:
- A $4 \times 4 \times 4$ cube has an even number of unit cubes along each dimension.
- Each block consists of 4 unit cubes, which is also an even number.
- Since both the cube and the blocks have even dimensions, it is possible to arrange the blocks to fill the cube without violating parity constraints.

4. Constructive Approach:
- One way to visualize the construction is to consider the $4 \times 4 \times 4$ cube as composed of smaller $2 \times 2 \times 2$ sub-cubes.
- Each $2 \times 2 \times 2$ sub-cube contains 8 unit cubes, which can be filled by 2 blocks of 4 unit cubes each.
- By arranging the blocks within each $2 \times 2 \times 2$ sub-cube and ensuring that the blocks fit together across the boundaries of these sub-cubes, we can fill the entire $4 \times 4 \times 4$ cube.

5. Conclusion:
- Given that the volume and parity constraints are satisfied, and that it is possible to arrange the blocks within smaller sub-cubes, it is indeed possible to build a $4 \times 4 \times 4$ cube from blocks consisting of 4 unit cubes.

The final answer is True