Directions: Determine the missing number that logically completes the following mathematical sequence.

8, 64, 512, 1000, ?, 8000, 15625

The correct answer is 3375.

To determine the missing number that completes the sequence, let us analyze the given mathematical series:
8, 64, 512, 1000, ?, 8000, 15625

First, observe that each term in the sequence is a perfect cube of a base number:

$2^3=8$

$4^3=64$

$8^3=512$

${10}^3=1000$

${20}^3=8000$

${25}^3=15625$

Now, let us examine the sequence formed by the base numbers:
2, 4, 8, 10, ?, 20, 25

The missing base corresponding to the unknown position is 15.

To find the missing term in the sequence, we compute the cube of 15:

${15}^3=15\times 15\times 15=3375$

Therefore, the missing number in the sequence is 3375.