"Bath Time!" the music mogul captioned the picture of 4-month-old Eric in the tub.
Cowell, 54, and Laura Silverman welcomed Eric on February 14 after the two had a scandalous affair while she was still married to Cowell's best friend, Andrew Silverman.
The former X Factor judge told the Mirror in April that he regretted how his relationship with Silverman began, but was happy to be a father.
Eric is Cowell's first son and the second for Silverman, who has a 7-year-old son from her previous marriage.
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