Determine the expanded form of the expression $(7+h)^{3}$: $(7+h)^{3}$

Step 1 ：We are given the expression \((7+h)^{3}\) and we are asked to expand it.

Step 2 ：We can use the binomial theorem to expand this expression. The binomial theorem states that \((a+b)^n = \sum_{k=0}^{n} {n \choose k} a^{n-k} b^{k}\). In this case, our 'a' is 7, 'b' is h, and 'n' is 3.

Step 3 ：Applying the binomial theorem, we get \(h^{3} + 21h^{2} + 147h + 343\).

Step 4 ：Thus, the expanded form of the expression \((7+h)^{3}\) is \(\boxed{h^{3} + 21h^{2} + 147h + 343}\).