William's parents are said to be, but they cannot be:
Father:  (Johann) Jacob CUPP
Mother:  Sibby BREEDING
In the 1820 census, there is no room for a male child William's age in Jacob & Sibby's household.  Jacob did not move to Laurel Co., KY (which is nowhere near Mason Co.), until after 1840; in other words, none of Jacob's children was born in KY.  In the 1880 census, William gives his father's birthplace as PA and his mothers as MD, but while Jacob was born in PA, Sibby was born in NC.

Many secondary sources give William a middle initial, "B," but I've yet to find a primary record where such a middle initial is used. 

There were no CUPPs in Mason Co., KY, in 1810, but there were three in 1820:  Phillip CUPP, Peter CUPP, and Mrs. CUPP (mis-indexed as Wm.), who were the only CUPPs in Kentucky in 1820.  Of the three, only Philip had a son William's age in the 1820 census.  Yet, when Philip moved on to Franklin Co., IN, by the 1840 census, William remained in Mason Co., KY, where he is found in the 1850 and 1860 censuses.  In the 1870 and 1880 censuses, William is in Missouri. 

1.  Jordan R. Dodd, ed.  1993.  Kentucky Marriages:  Early to 1850.  Liahona Research, Orem, UT (Broderbund CD-229):

Cupp, William

Jenkins, Letitia R.

2 Oct 1838

Mason Co.

William is the only male CUPP married in Mason County by 1850, at least, based on this CD.  The only female CUPP marriage in Mason County was Sarah CUPP to George JENKINS in 1845; yet, Sarah appears not to be William's sister.

2.  1840 Census Index and Digital Images (online at Ancestry.com; Image #13 of 40; extracted by Diana Gale Matthiesen):•

1840

KY

Mason Co.

Northern Division

pp. 7B-8A

Willm Copp

000 010 - 000 010

0100000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	20-29	1810-1820	= William (b. 1813)
1 female	20-29	1810-1820	= Letitia (b. 1816)
1	person engaged in agriculture

William is the only CUPP in the county.  Living next door to Hezekiah JENKINS.

3.  1850 Census Index/Microfilm (online at GenealogyLibrary.com):  District No 2, Mason Co., KY, p. 87, 429/429, enumerated 5 Sep 1850 (extracted by Diana Gale Matthiesen):•

William Cupp	36	M	Farmer	600	Ky
Leticia   "	34?	F			Ky
Margarett "	6	F			Ky
Sarah     "	4	F			Ky
George    "	9/12	M			Ky

Living two doors down from Hezekiah JENKINS (b. 1800, MD), who is too young to be Letitia's father, but who could be her brother.

4.  1860 Census Images (online at Ancestry.com; Image #140 of 366):  Orangeburg P.O., District No. 2, Mason Co., KY, p. 140, PN 140, 1012/991, enumerated 10 Jul 1860 (extracted by Diana Gale Matthiesen):•

William Cupp	48	M		Farmer	1500	650	Kentucky
Letetia	42	F					Do
Hannah M	16	F					Do
Sarah S	14	F					Do
George W	10	M					Do
John W	8	M					Do
Millard	4	M					Do
Martha A	1	F					Do

5.  1870 Census Index/Images (online at Genealogy.com; Image #48 of 74):  Trenton P.O., Trenton Twp., Grundy Co., MO, Roll 777 (Book 1), p. 388B, PN 48, 342/347, enumerated 22 Aug 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):

Cupp William	57	M	W	Farmer	2100	450	Ky
____ Letitia B	54	F	W				Ky
____ Hannah M	26	F	W				Ky
____ Sarah S	24	F	W				Ky
____ John W	18	M	W				Ky
____ Millard W	13	M	W				Ky
____ Martha A	10	F	W				Ky

6a.  1880 United States Census and National Index (LDS Family History Resource File: CD-ROM Library):

Census Place: Jackson, Grundy, Missouri
Source: FHL Film 1254688; NARA Film T9-0688; Pg 464C
	Relation	Sex	Marr	Race	Age	Birthplace	Occupation	Fa	Mo
Wm. CUPP	Self	M	M	W	67	KY	Farmer	PA	MI
L. R. CUPP	Wife	F	M	W	63	KY	Housekeeping	MI	MI
S. S. CUPP	Dau	F	S	W	33	KY		KY	KY
Jas. W. CUPP	Son	M	S	W	27	KY	Farm Hand	KY	KY

It was "Md," not "MI" (see next source).

6b.  1880 Census Images (online at Ancestry.com; Image #3 of 11):  Jackson Twp., Grundy Co., MO, p. 464C, PN 3, SD 7, ED 218, enumerated 2/3 Jun 1880 (extracted by Diana Gale Matthiesen):

1880:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).

1

2

3

4

5

6

8

9

10

13

15

20

24

25

26

24

25

Cupp Wm

W

M

67

/

Farmer

Ky

Pa

Md

____ L R

W

F

63

Wife

/

Housekeeping

Ky

Md

Md

____ S S

W

F

33

Daughter

/

Ky

Ky

Ky

____ Jas W

W

M

27

Son

/

Farm Hand

Broken Leg

/

Ky

Ky

Ky