To cube the expression $(7m + 4n)$, we apply the binomial expansion formula for $(a + b)^3$:

$(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$

For $(7m + 4n)$, $a = 7m$ and $b = 4n$. Substituting these into the formula:

$(7m + 4n)^3 = (7m)^3 + 3(7m)^2(4n) + 3(7m)(4n)^2 + (4n)^3$

Now calculate each term:

1. $(7m)^3 = 343m^3$
2. $3(7m)^2(4n) = 3(49m^2)(4n) = 588m^2n$
3. $3(7m)(4n)^2 = 3(7m)(16n^2) = 336mn^2$
4. $(4n)^3 = 64n^3$

Putting it all together:

$(7m + 4n)^3 = 343m^3 + 588m^2n + 336mn^2 + 64n^3$

Would you like more details or have any questions? Here are 5 related problems to consider:

1. Cube the expression $(3x + 5y)$.
2. Expand $(2a + 3b)^3$ step by step.
3. What is the expansion of $(x - y)^3$?
4. Find the cube of $(5p + 6q)$.
5. Expand $(x + 2)^3$.

Tip: Remember that the binomial expansion formula can be applied to powers beyond cubes, such as for squaring or fourth powers!