Not sure if this is your Alexander Cummings, as there seemed to be a difference in birth years and places. There were several Alex and Elizabeth Cummings in IL, so I went by Elizabeth and children that matched. Needs lots of research , but he did exist.
1850 United States Federal Census
View 1850 United States Federal Census
Name: Alexander Cummins
Age: 36
Birth Year: abt 1814
Birthplace: Tennessee
Home in 1850: District 10, Jefferson, Illinois, USA
Gender: Male
Family Number: 626
Household Members:
Name Age
Alexander Cummins 36
Elizabeth Cummins 22
Martha R Cummins 2
Matilda J Cummins 2
George W Cummins 0
Alexr Cumings
in the 1860 United States Federal Census
View 1860 United States Federal Census
Name: Alexr Cumings
Age: 32
Birth Year: abt 1828
Gender: Male
Birth Place: Ireland
Home in 1860: Between the Creeks, Greene, Illinois
Post Office: Carrollton
Dwelling Number: 1078
Family Number: 1078
Occupation: Farm Rent
Personal Estate Value: 50
Cannot Read, Write: Y
Household Members:
Name Age
Alexr Cumings 32
Elizabeth Cumings 31
Matilda Cumings 13- also listed as martha
Maletna Cumings 13
C C D Cumings 11- Christopher
George W Cumings 9
Orlando Cumings 2
1870 United States Federal Census
View 1870 United States Federal Census
Name: A Cummings
Age in 1870: 45
Birth Year: abt 1825
Birthplace: Illinois
Dwelling Number: 76
Home in 1870: Woodville, Greene, Illinois
Race: White
Gender: Male
Occupation: Farmer
Male Citizen over 21: Y
Personal Estate Value: 200
Real Estate Value: 1200
Inferred Spouse: E Cummings
Household Members:
Name Age
A Cummings 45
E Cummings 35
C Cummings 22
George Cummings 16
A Cummings 11
Nony Cummings 9
J Cummings 5 listed as living next door with Henry Ambrose Family
1880 United States Federal Census
View 1880 United States Federal Census
Name: Alex Cummings
Age: 58
Birth Date: Abt 1822
Birthplace: Illinois
Home in 1880: Greene, Illinois, USA
Dwelling Number: 56
Race: White
Gender: Male
Relation to Head of House: Self (Head)
Marital status: Married
Spouse's name: Elizabeth Cummings
Father's Birthplace: Illinois
Mother's Birthplace: Kentucky
Occupation: Farmer
Months Not Employed: 12
Neighbors:
Household Members:
Name Age
Alex Cummings 58
Elizabeth Cummings 52
Jacob Cummings 15
Son George W Cummings, married a Virginia Ambrose
Geo W Cummings
Gender: Male
Marriage Date: 7 Nov 1875
Marriage Place: Greene, Illinois, USA
Spouse: Virginia Ambrose
Film Number: 001310037
Mother Elizabeth was living with them in 1900
1900 United States Federal Census
Name Age
George Cummings 46
Virginia Cummings 40
Charles S Cummings 21
Henry W Cummings 10
Gordon L Cummings 8
Elizabeth Cummings 71
Elizabeth Cummings
Age: 71
Birth Date: Jul 1828
Birthplace: Kentucky
Home in 1900: Woodville, Greene, Illinois
Sheet Number: 3
Number of Dwelling in Order of Visitation: 50
Family Number: 50
Race: White
Gender: Female
Relation to Head of House: Mother
Marital status: Widowed