Goodwill and Intangible Assets - Amortization (Details) - USD ($) $ in Thousands	3 Months Ended	6 Months Ended
Feb. 28, 2026	Feb. 28, 2025	Feb. 28, 2026	Feb. 28, 2025	Aug. 31, 2025
Goodwill and Intangible Assets Disclosure [Abstract]
Amortization related to intangible assets	$ 171,754	$ 152,162	$ 324,201	$ 312,376
Finite-Lived Intangible Assets, Amortization Expense, Maturity Schedule [Abstract]
Remainder of 2026	298,607		298,607
2027	545,673		545,673
2028	506,276		506,276
2029	409,819		409,819
2030	311,173		311,173
Thereafter	476,986		476,986
Net Carrying Amount	$ 2,548,534		$ 2,548,534		$ 2,410,755

Finite-Lived Intangible Asset, Expected Amortization, After Year Four

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The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets.

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in remainder of current fiscal year.

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount after amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

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