Complete the analogy.
8:256::27:_____________?

Let's find the logic for the first pair $8:256$:
$$8\times 32=256$$

Alternatively, check power patterns:

$$8=2^3$$

$$256=4^4=2^8$$

Another simple logic:

$$\frac{x^2}{2}⟹\frac{8^2}{2}=32\text{ (not matching 256)}$$

Let's check:

$$x\times x^2=x^3⟹8^2\times 4=256$$

More precisely:

$$\text{Pattern is }x\to x\times 32$$

If $x=27$, then $27\times 32=864$ (not in options).

Let's look at another relation:

$$256=4^4=(8/2{)}^4$$

Let's check if $x\to (x{)}^2\times 4⟹8^2\times 4=256$.
Applying this to $27$:

$$27^2\times 4=729\times 4=2916$$

Let's check:

$$256=8^{\frac{8}{3}}\text{ (not an integer)}$$

Let's look closely at Option A ($6561$):

$$6561=9^4=(27/3{)}^4$$

For the first term: $8\to$ if rewritten as $8$, $(8\text{ is not divisible by 3})$.
Let's analyze $6561$ as $27^2\times 9=729\times 9=6561$.
For $8$: $8^2\times 4=256$. Here, $4$ is $\frac{8}{2}$ and $9$ is $\frac{27}{3}$.
Thus the logic is:

$$\text{Result}=x^2\times \sqrt[3]{x}$$

* For $8$: $8^2\times \sqrt[3]{8}=64\times 2=128\ne 256$.
Let's try:

$$\text{Result}=x\times 32⟹8\times 32=256$$

What about $6561$? $6561=27^{2.66}$
Let's look at $6561=3^8$. Since $27=3^3$, if $8=2^3\to 256=2^8$.
Wow! The pattern is:

$$x=a^3⟹\text{Output}=a^8$$

* For $8=2^3⟹2^8=256$.
* For $27=3^3⟹3^8=6561$.