Which Inca ruler was the father of both Huáscar and Atahualpa?

Huayna Capac was the Inca ruler who fathered both Huáscar and Atahualpa.

He was the eleventh Sapa Inca and ruled Tawantinsuyu during the early sixteenth century, when the empire reached its greatest territorial extent. His campaigns and administration strengthened Inca control across the Andes, including large parts of present-day Ecuador.

Huayna Capac died around 1527, probably during an epidemic associated with newly introduced European diseases. His designated heir, Ninan Cuyochi, also died, leaving the succession disputed. Huáscar controlled the imperial heartland around Cusco, while Atahualpa commanded powerful forces in the north.

Their rivalry became the Inca Civil War, which weakened the empire just before Francisco Pizarro's conquest. A common mix-up is confusing Huayna Capac with Túpac Inca Yupanqui: Túpac was Huayna Capac's father, not the father of the two brothers featured in the question.