In the following question, select the missing number from the given series.27 125 343 64 216 ? 7 11 16

Let's carefully rewrite the given pattern by separating the sequence into columns or related groups. Notice that the text string represents a combination of perfect cubes and their corresponding cube roots:
$$\text{Group 1: }27\to 3^3\text{ and its base root is }3$$
$$\text{Group 2: }125\to 5^3\text{ and its base root is }5$$
$$\text{Group 3: }343\to 7^3\text{ and its base root is }7$$
$$\text{Group 4: }64\to 4^3\text{ and its base root is }4$$
$$\text{Group 5: }216\to 6^3\text{ and its base root is }6$$
Let's examine the last set of digits: 7 11 16.Notice that these are sums of base pairs:$3+4=7$ (Base of Group 1 + Base of Group 4)$5+6=11$ (Base of Group 2 + Base of Group 5)Following this structure, the third sum is $16$. We know the base of Group 3 is $7$. Let the unknown base be $x$:
$$7+x=16⟹x=9$$
Since the upper numbers are perfect cubes of their bases, the missing term must be the cube of $9$:
$$9^3=9\times 9\times 9=729$$