Explanation:

Let’s break this down step by step.

- First pair is 1 : 7.

- 7 = 1³ + 6.

- Second: 3 : 215.

- 215 = 3³ + 3² × 7 + 8.

- Try the cube: 3³ = 27, not matching directly.

- Third to fourth: 4 : ?

- But let’s look for patterns with cubes:

- 1³ = 1, 1³ + 6 = 7.

- 3³ = 27; not matching 215.

- Let’s notice something more:

- Compare the numbers:

- 1, 7

- 3, 215

- 4, ?

- On closer look, 215 = 3³ + 64 = 27 + 188? No, let's try 3³ × 8

- 3³ = 27; 27 × 8 = 216, almost matches 215 (one less).

- 1³ × 7 = 1 × 7 = 7 (matches first pair).

- Pattern here: First number cubed × (next number, which is the second in pair) = second number.

- 1³ × 7 = 7

- 3³ × 8 = 27 × 8 = 216 (but pair is 215).

- Looks like the pattern might be: (first number)³ × (first number + 6) - 1.

- 3³ × (3 + 4) - 1 = 27 × 7 - 1 = 189 - 1 = 188, still not matching.

- Actually, let’s check the options for 4:

- Options:

- 453

- 342

- 511

- 363

- Now let’s try: 4³ × (4 + 3)

- 4³ = 64; 4 + 3 = 7

- 64 × 7 = 448

- 448 is close to option 1 (453), but not exact.

- Try 511:

- If try 4³ × 8 = 64 × 8 = 512

- 511 is just one less, as in the second case with 3: 3³ × 8 = 216, actual given is 215.

- So, the pattern is: (number)³ × (number + 4) - 1

- For 3: 3³ × (3 + 5) - 1 = 27 × 8 - 1 = 216 - 1 = 215

- For 4: 4³ × (4 + 4) - 1 = 64 × 8 - 1 = 512 - 1 = 511

So, the correct answer is:

511 (Option 3)

Here's what’s going on with each pair:

- 1 : 7 ? 1³ × 7 = 7

- 3 : 215 ? 3³ × 8 - 1 = 215

- 4 : 511 ? 4³ × 8 - 1 = 511