Joseph Sparhawk had four children —
Timothy, Joseph, Elizabeth, born 1742, and Hannah.

Joseph's first cousin Nathaniel Sparhawk married Elizabeth Pepperrell, daughter of Sir William Pepperrell.

Sparhawk —
History of Cambridge
http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A2001.05.0228%3Achapter%3D25%3Apage%3D657

Hannah⁵ Sparhawke Town Kinney, daughter of Joseph⁴ (Samuel³, Nathaniel², Nathaniel¹) Sparhawk, was born April 1738
Hannah Sparhawke married Edmund Town and resided at Sutton. Hannah's second husband was Reuben Kinney.
https://books.google.com/books?id=qFEhAQAAIAAJ&q=Sparhawk#v=snippet&q=Sparhawk&f=false

Timothy⁵ Sparhawk, son of Joseph⁴ (Samuel³, Nathaniel², Nathaniel¹) Sparhawk, was born March 13, 1751
Revolutionary soldier Timothy Sparhawk
Timothy was "brought up" living with Ebenezer Locke. On February 4, 1778, Timothy⁵ Sparhawk married Mary, daughter of Asa Conant, and had children. Mary Conant Sparhawk died in "middle life" i.e. in her middle age years. Timothy⁵ Sparhawk took care of his father-in-law Asa Conant and his wife in their old age. On October 17, 1817, Timothy⁵ married Mrs. Nancy Williams. She died May 18, 1823. Timothy⁵ Sparhawk died December 24, 1838. He was nearly 90 years old.
Children of Timothy⁵ Sparhawk and Mary Conant Sparhawk:
• Sally⁶ Sparhawk married William Story. They lived in Ashford, Connecticut. Seven children named in "The History of Oxford, Massachusetts" are William Story and Fitch Story moved to Ohio; Minor Story was a railroad contractor; named without further information are: Stephen Story; Danforth Story; Irene Story; Sally Story.
• Samuel⁶ Sparhawk died at New Lebanon, New York.
• Danforth⁶ Sparhawk married, at New Lebanon, New York, to Abigail Harwood of Cavendish, Vermont. Three daughters - all had died 1885.
• Sylvanus⁶ Sparhawk married Arvilla Riggs and settled at New Lebanon, New York. Many children.
• Martha⁶ Sparhawk, born 1797, married Thomas Kendall of New Lebanon, New York.
• Hannah⁶ Sparhawk, born about 1801, married Elijah Rich who died May 1, 1860. In 1885, Hannah⁶ lived at New Lebanon, New York. Several children.
• Mary⁶ Sparhawk was married on December 20, 1810, to Joseph Childs of Oxford, Massachusetts.
• Elizabeth⁶ Sparhawk died at Oxford, Massachusetts, on February 28, 1854, unmarried.
https://books.google.com/books?id=qFEhAQAAIAAJ&q=Sparhawk#v=snippet&q=Sparhawk&f=false

Joseph⁵ Sparhawk, son of Joseph⁴ (Samuel³, Nathaniel², Nathaniel¹) Sparhawk, was born August 16, 1754
Revolutionary soldier Joseph⁵ Sparhawk.
Joseph⁵ lived in the home of Captain Isaac Hartwell. On May 25, 1771, Capt. Hartwell records that Patience Lamson has begun her service with him. Also in 1771, on June 12, Capt. Hartwell records that Joseph⁵ Sparhawk has gone to Cambridge. On May 12, 1772, Joseph⁵ Sparhawk married Patience Lamson. She, like Joseph⁵, had been living with Capt. Isaac Hartwell. Joseph⁵ Sparhawk (son of Joseph⁴) died on November 7, 1807. His wife PatienceLamson Sparhawk died February 23, 1825, at Ward. Children of Joseph⁵ Sparhawk and Patience Lamson Sparhawk were:
• Ezra Sparhawk born November 5, 1773.
• Sarah⁶ Sparhawk born September 30, 1776.
• Hannah⁶ Sparhawk, born December 30, 1778. Married __ Fisher, a sea captain, had no children.
• Lucinda⁶ Sparhawk, born April 17, 1780. Married James Baldwin of Leicester. Children Lucy and John.
• Joseph⁶ Sparhawk married Rebecca, daughter of Ebenezer Davis, no children.
• John⁶ Sparhawk, born September 7, 1787. He did not marry. John⁶ Sparhawk drowned at Worcester on July 31, 1805.
• Elizabeth⁶ Sparhawk, born May 4, 1789, was married on May 20, 1807 to Timothy Kimball of Douglas.
https://books.google.com/books?id=qFEhAQAAIAAJ&q=Sparhawk#v=snippet&q=Sparhawk&f=false

Elizabeth⁵ Sparhawk, daughter of Joseph⁴ (Samuel³, Nathaniel², Nathaniel¹) Sparhawk was born 1742.
https://books.google.com/books?id=qFEhAQAAIAAJ&q=Sparhawk#v=snippet&q=Sparhawk&f=false

—

"History of the Town of Oxford, Massachusetts: With Genealogies and Notes on Persons and Estates", by George Fisher Daniels, author, with the co-operation of the town, 1892 - Oxford (Mass.) - Page 698:
https://books.google.com/books?id=qFEhAQAAIAAJ&q=Sparhawk#v=snippet&q=Sparhawk&f=false

Samuel and Sarah Whiting's son Joseph Sparhawk was married first to "Miss Cook"
She may have been Mary Cooke or Cook, and she may have been a descendant of Henry Cooke and Judith Birdsall Cook according to a Geni family tree.

At WkTree, the wife "Elizabeth Cook" and the Cook lineage given to "Miss Cook" (the wife of Joseph Sparhawk 1708) are incorrectly attached to Joseph Sparhawk and not accurate. Joseph Sparhawk 1708 DID NOT marry an "Elizabeth Cook from Isle of Wight, Virginia".

see notes above
COOKE / COOK
Henry Cook
Judith Birdsall

John Cook
Mary Buxton

John Cooke
Hannah Deane

Mary Cook
https://www.geni.com/people/Mary-Sparhawk/6000000037130604376
Joseph Sparhawk
https://books.google.com/books?id=qFEhAQAAIAAJ&q=Sparhawk#v=snippet&q=Sparhawk&f=false

Timothy Sparhawk, NSDAR #A107842
Mary Conant
https://services.dar.org/Public/DAR_Research/search_adb/default.cfm?action=full&p_id=A107842
Timothy Sparhawk next married Mrs. Nancy Williams
https://books.google.com/books?id=qFEhAQAAIAAJ&q=Sparhawk#v=snippet&q=Sparhawk&f=false

Joseph's second wife "Miss Sibley" is said to be Elizabeth Sibley which is plausible. No clear answer to what children were born to which wife; however this (and more) can possibly be ascertained with careful reading and research.

History of Cambridge, Massachusetts, 1630-1877: With a Genealogical Register
By Lucius Robinson Paige
H. O. Houghton, 1877 - Cambridge (Mass.) - 731 pages