AMC 12A 2023 (Problem 12)What is the value of 23−13+43−33+63−53+⋯+183−1732^3-1^3+4^3-3^3+6^3-5^3+\cdots+18^3-17^323−13+43−33+63−53+⋯+183−173?(A) 2023\text{(A)}\;2023(A)2023(B) 2679\text{(B)}\;2679(B)2679(C) 2941\text{(C)}\;2941(C)2941(D) 3159\text{(D)}\;3159(D)3159(E) 3235\text{(E)}\;3235(E)3235Related TopicsToolkit 3 — Sum of cubesHints (3)Hint 1Rewrite as −(13+23+⋯+183)+2(23+43+63+⋯+183)-(1^3+2^3+\cdots+18^3)+2(2^3+4^3+6^3+\cdots+18^3)−(13+23+⋯+183)+2(23+43+63+⋯+183).Hint 2Use Identity 3. Sum of Cubes: 13+23+⋯+n3=(n(n+1)2)2.1^3+2^3+\cdots+n^3=\left(\frac{n(n+1)}{2}\right)^2.13+23+⋯+n3=(2n(n+1))2.Hint 3Note 23+43+63+⋯+183=8(13+23+⋯+93)2^3+4^3+6^3+\cdots+18^3=8(1^3+2^3+\cdots+9^3)23+43+63+⋯+183=8(13+23+⋯+93).Final Answer(D) 3159