Solution
= Solution
If $V$ is the defining representation, $χ_V=2t$. The character of $\operatorname{Sym}^3V$ is $(2t)^3-2(2t)=8t^3-4t$. Therefore $8t^3$ is the character of $\operatorname{Sym}^3V\oplus V\oplus V$.
= Solution
If $V$ is the defining representation, $χ_V=2t$. The character of $\operatorname{Sym}^3V$ is $(2t)^3-2(2t)=8t^3-4t$. Therefore $8t^3$ is the character of $\operatorname{Sym}^3V\oplus V\oplus V$.