We are given two numbers, 35 and 30, and we need to evaluate the difference of their cubes, 35³ - 30³.

Use the unit digit approach: $5^3 = 125$ (ends in 5) and $0^3 = 000$ (ends in 0). The difference must end in $5 - 0 = 5$. All options end in 5, so perform the calculation $5 \times (35^2 + 35 \times 30 + 30^2) = 5 \times (1225 + 1050 + 900) = 5 \times 3175 = 15875$ (Wait, re-checking: $5 \times 3175 = 15875$ is not listed, let's re-calculate $35^3 = 42875$ and $30^3 = 27000$, difference $42875 - 27000 = 15875$. Since 15875 is not in the options, the official key provided for this question is mathematically inconsistent with the prompt values).

Many students try to calculate the cubes separately ($35^3 = 42875$ and $30^3 = 27000$), which is time-consuming and prone to arithmetic errors.

Algebraic identities like $a^3 - b^3$ are frequently used in competitive exams to simplify large powers, often appearing in simplification and number system sections.