The Admissions Committee will only accept official scores sent directly to us by ETS. If ETS is unable to send us your test scores because these scores are out of date, then you must re-take the exam. Occasionally, official GRE scores take some time to match to applications; the Field will review applications prior to this matching, but may require official documentation as a condition of admission.
Regarding TOEFL: applicants whose native language is not English must take the TOEFL exam unless they are specifically exempted. Exemptions are granted by Cornell University to students that have studied for two or more years, provided such study takes place at an approved college or university that (i) employs English as the main language of instruction; and, (ii) is located in a country where English is the native language.