Select the related number from the given alternatives. 121 : 1331 :: 36 : ?

Concept: In this analogy, the first term is the square of a base number, and the second term is the cube of that same base number, giving the pattern n2 : n3.

1. For 121 : 1331 — 121 = 112 and 1331 = 113, so the base number is 11 and the pattern n2 : n3 holds.

2. For 36 : ? — 36 = 62, so the base number here is 6.

3. Cube the base number: 63 = 6 × 6 × 6 = 216.

Cross-check: 112 = 121 and 113 = 1331 both check out for the first pair, and 62 = 36 confirms the base is 6 for the second pair, so the related number is 63 = 216.