Cobb-Douglas utility functions are definitionally homothetic because they represent monotonic transformations of homogeneous functions of degree one, meaning marginal rates of substitution depend only on the ratio of consumption quantities rather than total income or utility.
The claim that Cobb-Douglas preferences are homothetic is a foundational, axiomatic mathematical property in microeconomics. It is trivially true by definition and standard consumer theory, requiring no empirical citation as it is a deductive mathematical fact.