1. We are asked to calculate the function $x^3$ using summations. 2. The function $x^3$ can be expressed as the sum of the first $x$ squares using the formula: $$x^3 = \sum_{k=1}^x (3k^2 - 3k + 1)$$ 3. This formula comes from the identity that the sum of cubes equals the square of the sum of the first $x$ natural numbers: $$\left(\sum_{k=1}^x k\right)^2 = \left(\frac{x(x+1)}{2}\right)^2 = x^3$$ 4. To verify, let's calculate $x=3$: $$\sum_{k=1}^3 (3k^2 - 3k + 1) = (3\cdot1^2 - 3\cdot1 + 1) + (3\cdot2^2 - 3\cdot2 + 1) + (3\cdot3^2 - 3\cdot3 + 1)$$ $$= (3 - 3 + 1) + (12 - 6 + 1) + (27 - 9 + 1) = 1 + 7 + 19 = 27$$ 5. Since $3^3 = 27$, the summation correctly calculates $x^3$. Final answer: The function $x^3$ can be calculated using the summation formula: $$x^3 = \sum_{k=1}^x (3k^2 - 3k + 1)$$