Let's break down and solve the expression:

$-3(-1)^3 - (-4)$

Step 1: Simplify the exponent

$(-1)^3 = -1$

Step 2: Multiply $-3$ by $-1$

$-3 \times -1 = 3$

Step 3: Simplify the double negative

The expression now looks like: $3 - (-4)$ This becomes: $3 + 4 = 7$

So, the solution to the expression is: $\boxed{7}$

Would you like any further details or have any questions?

Here are five related questions:

1. What happens when you square $(-1)$ instead of cubing it?
2. How would the expression change if the base of the exponent was positive?
3. Can you simplify $-3(-2)^3 + 4$?
4. How do double negatives work in algebra?
5. How does exponentiation of negative numbers differ with even and odd exponents?

Tip: Be careful with signs in calculations, especially with exponents and negatives.