McCubbin's wife, Brandy, said their five-year-old daughter, Kenley, named the calf Lucky because she's lucky to be alive.
"From a distance, I thought I had twins lying together," said Stan McCubbin.
"I saw two noses. I thought it was twins and then when I saw her, I was just completely blown away."
Mr McCubbin's wife, Brandy, added: "He was just like: "I've got a two-headed calf", so I was in shock."
The couple conceded that it was therefore not hard to find a name for the baby cow.
"I said she was lucky to live, and our little five-year-old, Kenley, said 'That's her name - Lucky'," said Brandy McCubbin.
"She is lucky and we're blessed to have this happen on our farm."
However, the family are also prepared for the fact that Lucky may not live very long.
"I'm just thinking: "How many days do we have?" And I mean, it's a blessing that we get to go through this with our children and our family and it's just something unique and rare," said Brandy McCubbin.
Stan McCubbin: "It's something I've never seen before and I think it's amazing. I think it's something these kids will get to remember forever."