Sum of odd cubes

Find by the method of Undetermined Coefficients the sum of $1^{3} + 3^{3} + 5^{3} + 7^{3} + \dots to n terms.$

~10 minAnswer checked instantlyseries sumundetermined coefficients

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXII. Undetermined Coefficients, Examples XXII.a, No. 4

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).