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The Babylonians solved cubic functions with the help of tables and the remains were found on engraved tablets.
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Baskara II contributed to solving cubic equations along with many other mathematical contributions.
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Quin Jiushao solves cubic equations in his book Shushu Jiuzhang.
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Omar Khayyam helped in developing theories of cubic functions. These theories were published in Treatise on Demonstration of Problems of Algebra
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Wang Xiaotong solved 25 cubic functions
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Archimedes solved cubic equations in his work with spheres and cylinders
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Hippocrates reduced duplicating the cube
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Menaechmus made developments in using conics for solving cubic equations
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Fibonacci finds a solutions to a cubic equation
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He solved the depressed cubic equation.
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Tartaglia claimed a solution to two cubics
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View contributed to the history by deriving the trigonometric solution for the cubic equation with three real roots
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Descartes summarized and extended the Viète’s study
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Cardano published Tartaglia's work. This method for solving cubics is known as the Cardano’s method