1. **State the problem:** We need to find the value of $T$ that satisfies the equation $$\frac{T \times T \times T}{T + T + T} = 6.$$ 2. **Rewrite the equation:** The numerator is $T^3$ and the denominator is $3T$, so the equation becomes $$\frac{T^3}{3T} = 6.$$ 3. **Simplify the fraction:** Since $T \neq 0$, we can simplify $$\frac{T^3}{3T} = \frac{T^2}{3}.$$ 4. **Set up the simplified equation:** $$\frac{T^2}{3} = 6.$$ 5. **Solve for $T^2$:** Multiply both sides by 3 to isolate $T^2$: $$T^2 = 18.$$ 6. **Find $T$:** Take the square root of both sides: $$T = \pm \sqrt{18} = \pm 3\sqrt{2}.$$ 7. **Final answer:** The values of $T$ that satisfy the equation are $$T = 3\sqrt{2} \text{ or } T = -3\sqrt{2}.$$