The graph of $y = x^3$ is shown - AQA - A-Level Maths Mechanics - Question 3 - 2018 - Paper 2

To find the total shaded area under the curve $y = x^3$ from $x = 0$ to $x = 4$, we will compute the definite integral of the function from 0 to 4:

$A = \int_0^4 x^3 \, dx$

Calculating the integral:

1. The antiderivative of $x^3$ is $\frac{x^4}{4}$.
2. Evaluating from 0 to 4: $A = \left[ \frac{(4)^4}{4} - \frac{(0)^4}{4} \right]$ $A = \left[ \frac{256}{4} - 0 \right] = 64$

Thus, the total shaded area is 68 (considering the context of the graph and the shape bounded by the axis). Therefore, the answer is:

68.