Question Statement:
$\vec{v} = x^3 \hat{i} + y^3 \hat{j} + z^3 \hat{k}$ is a vector field where $\hat{i}, \hat{j}, \hat{k}$ are the base vectors of a Cartesian coordinate system. Using the Gauss divergence theorem, the value of the outward flux of the vector field over the surface of a sphere of unit radius centered at the origin is ______ (rounded off to one decimal place).
Scientific schematic diagram reproduced from official IIT paper