The sum of the cubes of two even numbers will always be an even number.

Explanation:

• Let the two even numbers be $2a$ and $2b$, where $a$ and $b$ are integers.
• The cube of an even number is $(2a)^3 = 8a^3$ and $(2b)^3 = 8b^3$.

Now, let's find the sum of these cubes: $(2a)^3 + (2b)^3 = 8a^3 + 8b^3 = 8(a^3 + b^3)$

The expression $8(a^3 + b^3)$ is clearly divisible by 8, which means it is an even number.

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Related Questions:

1. What is the sum of the cubes of two odd numbers?
2. Is the cube of an odd number always odd?
3. How do you prove that the cube of an even number is always even?
4. Can the sum of cubes of an even and an odd number ever be even?
5. What is the general form for the sum of cubes of two numbers?

Tip: When analyzing powers and sums involving even and odd numbers, remember that even numbers are always multiples of 2, which plays a crucial role in determining the parity (even or odd nature) of the result.