The text as a whole seems to me to be related.

THE CUCKOO
(Once very popular. This is the only version I have heard; it was sung by Elijah Iles, Inglesham, Wilts.--Williams)

The cuckoo is a merry bird,
He sings as he flies,
He brings us glad tidings,
And tells us no lies.

He sucks the birds' eggs
To make his voice clear,
And the more he cries "Cuckoo!"
The summer draws near.

The cuckoo is a lazy bird,
She never builds a nest,
She makes herself busy
By singing to the rest;

She never hatches her own young,
And that we all know,
But leaves it for some other bird While she cries "Cuckoo!"

And when her time is come
Her voice we no longer hear,
And where she goes we do not know
Until another year.

The cukcoo comes in April,
She sings a song in May,
In June she beats upon the drum,
And then she'll fly away.

(Alfred Williams, Folk Songs of the Upper Thames, 1923, p. 165; no music)

~Masato