As William Robinson is not with his father James and 2 siblings on 1881 census there are these 2 possible death entries
Mar 1873 Rochdale William Robinson age 0
Dec 1876 Rochdale William Robinson age 4
William Robinson Death Age:4
Burial 10 Nov 1876 Edenfield, Lancashire,
You can view the burial entry here https://www.familysearch.org/ark:/61903/3:1:S3HY-6LCN-TS?i=307 gives abode as Spotland, no details as to parents names
The death registration in 1876 of William Robison aged 4 was in Spotland sub-district.
www.lancashirebmd.org.uk/deathsearch.phpWilliam Robinson Death Age:4
Burial 10 Nov 1876 Edenfield, Lancashire,
You can view the burial entry here https://www.familysearch.org/ark:/61903/3:1:S3HY-6LCN-TS?i=307 gives abode as Spotland, no details as to parents names
The burial before William at Edenfield was 31st October 1876 Mary Robinson aged 8, abode Spotland.
www.lan-opc.org.uk/Bury/Edenfield/parishchurch/index.html
These may be baptisms of Mary and William at St. James, Ashworth:
2nd Aug. 1868 Mary Robinson daughter of William & Sarah. Abode Greenbooth. Occupation shepherd.
15th Sep. 1872 William Robinson son of William & Sarah Ann. Abode Shuttleworth. Occupation farmer.
Shuttleworth is near Edenfield.
Baptisms of other likely children of the couple:
1869 Henry. Abode Lower Naden
1870 Elizabeth. Abode Shuttleworth
1874 Richard Pye. Abode Cheesden Top Spotland
1876 Sarah Ann. Abode Spotland
William was a farmer on those 4 baptisms.
Lancashire Online Parish Clerks
www.lan-opc.org.ukBirths of Mary 1868, Henry 1869, and Richard 1874 were registered in Spotland sub-district, mother's maiden surname Howarth.
Elizabeth 1870 and William 1872 were registered in Walmersley sub-district, mother's maiden name Howarth. This fits with abode Shuttleworth at baptism as the township was Walmersley-cum-Shuttleworth.
Sarah Ann 1876 was registered in Spotland sub-district.
www.lancashirebmd.org.ukProbable marriage of parents William Robinson & Sarah Howarth 1867 St. Paul, Norden, Rochdale.
So, the William Robinson buried at Edenfield in 1876 was likely a son of William & Sarah and Mary who was buried 10 days earlier was probably their daughter.