1. There is no seaweed cake and no birthday cake.

2. There are no seaweed cake and no birthday cake.
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Do we have to use 'is' or 'are' in the sentences? Which one is grammatical?

I’d use the structure and verb in #1 even though it’s not 100% grammatically correct. However, I’d prefer to rephrase:

There is neither seaweed cake nor birthday cake.