I can't find the birth record of Edward though to get his parents names accurately.
I know his father is William from the marriage certificate.
Can you give us all the details from his 1906 marriage certificate?
What occupation for his father William?
Age if given & Address for Edward Davies
Did either witness have surname Davies
working from possible birth registrations for the children
Ada Davies dec qtr 1906 Pontypridd vol 11a pg 624
Ethel Evans june qtr 1898 Pontypridd vol 11a pg 574
mother's maiden name on both is Evans
Possible marriage
Samuel Evans sept qtr 1892 Pontypridd vol 11a pg 754 with Elizabeth Ann Evans on the same page
Possible death reg
Samuel Evans 35 march qtr 1900 Pontypridd vol 11a pg 388
Elizabeth as a widow on 1901 census - perhaps Edward Davies was living close by in Tonypandy area
72, Kinry Street, Tonypandy
Elizabeth Ann Evans Head Widow 1870 Pontypool, Monmouthshire, Wales
Willie Evans Son 1893 Tonypandy, Glamorganshire, Wales
Johnnie Evans Son 1895 Tonypandy, Glamorganshire, Wales
Ethel Evans Daughter. 1899 Tonypandy, Glamorganshire, Wales
John Mead Boarder Single 1855 Timberman Labourer Colliery Surface Gloucestershire
RG13 Piece 5017 Folio 103 Page 14