Learn French: Gardons ce gâteau pour demain. - Let's keep this cake for tomorrow.

Gardons is the nous (we) form of the regular verb garder (to keep). In French, to say "Let's" do something, you simply use the nous form of the verb without the pronoun.

Why is there no pronoun like nous before gardons?

Because this is an imperative (a command or suggestion). Just like in English where we say "Stop!" instead of "You stop!", French drops the subject pronouns (tu, nous, and vous) when giving commands or making "Let's" suggestions.

Why use ce instead of le before gâteau?

Ce means "this" or "that" for masculine nouns. If you used le, the sentence would mean "Let's keep the cake" instead of "Let's keep this cake."

How did we form the word gardons?

It comes from garder, which is a regular -er verb. To make the command form for nous, you just drop the -er and add the standard -ons ending.