。
I cannot live without eating pudding, I say.
Literal
I-[archaic 麿] [topic-は] pudding [object-を] not-eating-[concessive-ないでは] cannot-exist-[classical-おれぬ].
麿 (まろ) is an archaic first-person pronoun once used by Heian-period courtiers — surviving today mostly as an over-the-top affectation in fiction or comedy. ないではおれぬ is the classical version of the modern ないではいられない ('cannot refrain from doing X,' 'cannot help but X'). おれぬ is the classical negative of おる (a humble/classical form of いる, 'to exist'). The result: 'cannot not-eat pudding' = 'cannot help but eat pudding.' A comedic mismatch of lofty grammar with mundane pudding.