To shift the function \( f(x) = (x + 1)^3 \) to the left by three units, you need to replace \( x \) with \( x + 3 \) in the function. This adjustment accounts for the leftward shift in the graph.
So, the new function \( g(x) \) after shifting left three units is:
\[ g(x) = ((x + 3) + 1)^3 = (x + 4)^3 \]
Thus, the equation that describes the function after the shift is:
\[ g(x) = (x + 4)^3 \]