Edward Baker Eddie Lincoln was the second son of Abraham Lincoln and Mary Todd Lincoln. He was named after Lincolns friend Edward Dickinson Baker. Both his mother and father spelled his name Eddy the National Park Service uses Eddie, which is on his gravestone.
Authorship of the poem was long a mystery with some supposing that Abraham and Mary Lincoln wrote it. In 2012, the Abraham Lincoln Association published an article in their journal that concludes neither parent wrote the poem, and that it was instead an early draft by a young poet from St. Louis. The final line is on the boys tombstone. This is most likely a reference to Matthew 1914 KJV But Jesus said, Suffer little children, and forbid them not, to come unto me for of such is the kingdom of heaven. The next child of Abraham and Mary was born ten months after Eddies death. After the death of President Lincoln, his remains were transferred to the Lincoln Tomb at Oak Ridge Cemetery in Springfield.
Source: Wikipedia