the means of livelihood increase with the increase of sons/every son born brings his sustenance with him
The meaning is that when a son is born, his means of livelihood comes with him; every person is born with his sustenance. The newborn brings blessing and economic abundance with him.
(And Rabbi Yitzchak of the house of Rabbi Ami said: A male child comes into the world – his loaf comes in his hand, male – this is a loaf. – Niddah 70b)
Translation
Expression (Hebrew)
בָּא זָכָר לְעוֹלָם - בָּא כִּכָּרוֹ בְּיָדוֹ
Definition (Hebrew)
כַּאֲשֶׁר נוֹלַד בֵּן, פַּרְנָסָתוֹ מַגִּיעָה עִמּוֹ. כָּל אָדָם נוֹלַד עִם פַּרְנָסָתוֹ עִמּוֹ. הַתִּינוֹק מֵבִיא אִתּוֹ בְּרָכָה וְשֶׁפַע כַּלְכָּלִי.
(וְאָמַר ר' יִצְחָק דְּבֵי רַבִּי אִמִּי: בָּא זָכָר בָּעוֹלָם - בָּא כִּכָּרוֹ בְּיָדוֹ, זָכָר- זֶה כַּר"- נִדָּה לֹא ע"ב)