Google found 90+ copies of "The Box" on the Internet. More than half of them are associated with John Denver. John Denver recited "The Box" on his 1971 album "Poems, Prayers & Promises." At AMG - All Music Guide, authorship is credited to "Lascelles"--no other name given.

On the web sites that contain the poem, sometimes the author's name is given as "Lascelles," sometimes as "Lascelles Abercrombie," and sometimes as "Kendrew Lascelles." I'm betting that the latter is correct, because the Library of Congress lists a 40-page book called "The Box" by Kendrew Lascelles, copyright 1974. The Internet Movie Database (IMDb) lists Kendrew Lascelles as an actor and screenwriter. The Internet Broadway Database (IBDB) credits him for a couple of Broadway musicals.

(Lascelles Abercrombie, on the other hand, was a scholarly English poet and critic who died in 1938. His poetry was called "complex and cerebral in style" by the Columbia Encyclopedia.)

One source said Steve Martin recited this poem on the Smothers Brothers Show.

The poem has also been posted in the threads called
From a Mother's Point of View...
Greatest Anti-War Song Ever? and
Lyr Req: The Thing