Look vs. looks in specific example
Solution 1:
'Looks' isn't plural, the s at the end means that it is conjugated for the third person singular.
In the second sentence, look is an infinitive. This is because it doesn't have a subject, 'the cake' is the object of the verb 'make'. This is clearer if you use pronouns, for instance, 'I saw him(object) run(infinitive) away.