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.