The grammar isn't at issue the meaning is. In the kind of context you're talking about "last time" means the time immediately preceding now . ", your listener would think your were talking about the cake you ate on Wednesday.
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Anonymous"My arms gotten bigger since I went school, cuz last time the sleeves of this hoodie was bigger""Last time" is not very useful in this sentence -- it doesn't refer to anything specific. That's not the sentence's only problem, though. I see four errors (not counting the ambiguous "last time") -- want to try to correct them?