Perhaps someone else has posted this poem before, but I haven't been able to find it here.
It was written in honor of Alexei by the famous Russian poet Marina Tsvetaeva on the third day of Easter, April 4, 1917. The religious theme and imagery are very interesting (Alexei is linked to Christ on various levels), as is Tsvetaeva's concern that Alexei will share the fate of Tsarevich Dmitri of Uglich, who was murdered back in the sixteenth century.
I apologize for translating the poem literally from the Russian. You will have to take my word for it that it sounds very beautiful in the original. (I will post the Russian, too, upon request.)
For the Infant - for the Dove - for the Son,
For the young tsarevich Alexei
Pray, church-going Russia!
Wipe the tears from his angelic eyes,
Remember how the Uglich dove
Fell on the tiles - Dmitri!
You are tender, Mother Russia!
Oh, will you really not have for him
enough loving grace?
Do not punish the son for the sins of the father.
Oh, peasant Russia, preserve
The lamb of Tsarskoe Selo - Alexei!