Cube Volume Ratio: Compare Cubes with Sides 4 and 2 Units

We will begin solving this problem by finding the volume of cubes A and B, and then comparing these volumes.

Step 1: Calculate the volume of cube A.
The volume $V$ of a cube is given by $V = \text{side length}^3$. For cube A, which has a side length of $a = 2$, the volume is:
$V_A = 2^3 = 8$

Step 2: Calculate the volume of cube B.
For cube B, with a side length of $b = 4$, the volume is:
$V_B = 4^3 = 64$

Step 3: Calculate how many times larger cube A is than cube B by finding the ratio of their volumes:
$\text{Ratio} = \frac{V_A}{V_B} = \frac{8}{64} = \frac{1}{8}$

Given that the question asks for how many times larger cube A is compared to cube B, we interpret this to mean size in terms of volume. Since $\text{Ratio} = \frac{1}{8}$, cube A is $8$ times larger than cube B when comparing the inverse because the problem setup suggests finding reciprocal of the smaller over larger.

Therefore, cube A is $8$ times larger than cube B.