This BIRTH reg on FreeBMD?

Births Mar 1863
COOK William Westbury S 6a 213

Name: William Cook
Year of Registration: 1863
Quarter of Registration: Jan-Feb-Mar
District: Chepstow
County: Gloucestershire, Monmouthshire
Volume: 11a
Page: 15

Year: 1863
Month: Apr
Day: 3
Parents_Surname: COOK
Child_Forenames: William
Fathers_Forenames: Ebenezer Harris
Mothers_Forenames: Charlotte
Mothers_Surname:
Residence: Alvington
Occupation: Laborer [sic]
Officiating_Minister: W. Somerset Rector
Event: Baptism
Memoranda:
Notes:
Register_Reference: P12 IN 1/5
Page_Number: 13
Parish_Chapel: Alvington

would seem a posible explanation

Death registration
Name: William Cook
Year of Registration: 1863
Quarter of Registration: Apr-May-Jun
District: Chepstow
County: Gloucestershire, Monmouthshire
Volume: 11a
Page: 11

Year: 1863
Month: Apr
Day: 7
Surname: COOK
Forenames: William
Residence: Alvington
Age_at_death: 5 weeks
Officiating_Minister: William Somerset Rector
Event: Burial
Cause_of_death:
Memoranda:
Notes:
Register_Reference: P12 IN 1/8
Page_No: 46
Parish_Chapel: Alvington

1871
Ebenezer Cook abt 1826 Alvington, Gloucestershire, England Head Alvington, Gloucestershire
Charlotte Cook abt 1826 Alvington, Gloucestershire, England Wife Alvington, Gloucestershire
Ada Jane Cook abt 1861 Alvington, Gloucestershire, England Daughter Alvington, Gloucestershire
Ebenezer Cook abt 1866 Alvington, Gloucestershire, England Son Alvington, Gloucestershire
George Cook abt 1858 Alvington, Gloucestershire, England Son Alvington, Gloucestershire
Lucy E Cook abt 1869 Alvington, Gloucestershire, England Daughter Alvington, Gloucestershire

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Ἀριστοτέλης A Gloster Boy in the Forest of Dean ><((((*>

If you look in the parish records section, you will find that he was buried on April 7, 1863 in Alvington.