The answer to the main question asked is trivially yes; Russell was well aware of Kant's views on mathematics and was influenced by them. Kant, Frege and many others were forerunners to Russell's views on mathematics in a very general sense.
The answer to the more interesting question in the body of the text - whether Russell's conception of mathematics is analytic - is definitely no. Russell held that mathematics and logic are both synthetic. Kant on the other hand held that logic is separate from mathematics; logic is analytic and mathematics is synthetic. As Russell says:
Kant never doubted for a moment that the propositions of logic are
analytic, whereas he rightly perceived that those of mathematics are
synthetic. It has since appeared that logic is as synthetic as all
other kinds of truth...
The Principles of Mathematics, section 434
I would add that when you say Kant 'showed' mathematics is synthetic a priori, you seem to imply this was definitively done, but Kant's, Frege's and Russell's conceptions of mathematics and logic have been disputed by Quine, Wittgenstein and others.