To solve the expression \(4^3 : (0.8)^3\), we need to calculate the cube of 4 and the cube of 0.8 separately, and then divide the result of the first by the result of the second.
Step 1: Calculate \(4^3\)
We start by calculating \(4^3\):
\[
4^3 = 64
\]
Step 2: Calculate \((0.8)^3\)
Next, we calculate \((0.8)^3\):
\[
(0.8)^3 = 0.512
\]
Step 3: Perform the Division
Now, we divide the results from Step 1 and Step 2:
\[
\frac{64}{0.512} \approx 124.99999999999997
\]
Final Answer
Thus, the final result is approximately:
\[
\boxed{125}
\]