The 35-year-old "Girls Aloud" hitmaker tied the knot with now husband Justin Scott in January last year.
The two welcomed Cole last month, while Walsh gave birth to their first child Bobby, two, in September 2014 when they were not married, reported Female First.
"When Justin brought him in, Bobby start doing this little victory dance and was running around, singing 'My baby brother!' Then he bent down by his car seat and went, 'Aw, coochy, coochy, coo'.
"It was very sweet. I really wanted a little brother for Bobby, close in age, so I'm over the moon to have our two beautiful boys," Walsh told Hello! magazine.
"If it's anything like New Year, we'll be in bed with the TV and sicky muslins.
"But we had the most amazing wedding and to now have two beautiful, healthy sons is wonderful enough, so whatever we do, I'll be happy.
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