To solve the problem of finding the minimum number of cuts needed to divide a cube into 27 smaller cubes, we can follow these steps:

Key Observations:

27 smaller cubes mean each edge of the original cube must be divided into 3 equal parts (since (3^3 = 27)).

For any axis (length, width, height), splitting an edge into (n) parts requires ((n-1)) cuts. Here, (n=3), so each axis needs (3-1=2) cuts.

Total Cuts:

There are 3 axes (x, y, z). Thus, total cuts = (2 \times 3 = 6).

Answer: 6.

(\boxed{6})

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