Dave, I didn't want to sound discouraging or negative in my previous post, so I've just gone to see what I could find that was a definite place to start from.
First, Reuben's death.
I've found Reuben Levice's death recorded in Q3 (July-Aug-Sept) in 1864 in Huntingdon so that part is spot on. (Volume 3b, Page 145) Interesting that it's recorded as Levice not Levis, so we definitely need to be open on the spelling!
Second, the census:
1841 census: Reuben, again spelt Levice, is 15, (and the ages were often rounded up or down to the nearest 5 in 1841). In the same household is Ann Gregory age 55 and a second Ann Gregory age 25. The elder Ann is listed as a Butcher. They are living in Sawtry St Andrew, and all were born in Huntingdonshire.
1851 census: Reuben Levis is 25, and married to Mary. They are living in Sawtry with their children Alice, William and Rachel (which helps support your belief that his mother was Rachel). In the same household are John Shareman or Shoreman, with his wife and son. They are Lodgers.
I think the address is Horn Drove, and Reuben is an Agricultural Labourer.
1861: Still in Horn Drove. Reuben, Mary, William, Rachel, and younger children Mary Ann, Emma, Sarah and Reuben age 2. Alice is not listed and whilst that may mean she has died it could equally mean that she has moved out because by now she will be 15, and could possibly have gone into service or similar.
1871: Reuben has died, and Mary is Head of the household. The family has moved to Ramsay, and Mary is working as a Charwoman. Children still at home are William, Rachel, Sarah, Reuben, and two younger ones Aaron age 9 and John age 6. All the children are working as Agricultural Labourers, apart from John. (hopefully that's an error in regard to Aaron)
Finally, Birth, 1859: No doubt all the children's births are listed but I just searched Reuben's. First quarter of 1859, named Reuben John Levice. Vol 3B, P. 255.
Where to go from here? My suggestion would be that you start by ordering a copy of Reuben's death certificate from 1864 and hoping that there is a reference to his father on that, because that would get you off to a start for your search to confirm his parents. Good luck.