Mr. Radley had been lying to keep the gifts out of the knot-hole.

When the tree is filled with cement, it symbolizes the end of Boo Radley's attempts to communicate with the children.  He communicates with them through the gifts he leaves for them.  These gifts symbolize the friendship he extends to them.  When the tree is filled in, it symbolizes an obstacle in their friendship.

I don't believe Harper Lee had any underlying symbolic motives concerning the Radley oak tree in To Kill a Mockingbird. The tree and its knothole simply served as the secret message conduit between the children and Boo Radley. Boo's brother, Nathan, apparently observed either Boo or the children reaching into the knothole, and decided to investigate. He cemented the knothole not because the tree was sick, but in order to keep his brother from having any further contact with Jem and Scout. Jem discovered that Nathan's story about the tree being diseased was a lie when Atticus pointed out that it appeared perfectly healthy. I suppose the act of cementing the knothole--a kind of symbolic heart of the tree--could represent Boo's family's cold-hearted nature in general.

In chapter 7, Jem and Scout write a letter to the anonymous gift-giver who has been leaving small presents in the knothole of the Radleys's tree. Scout is too naïve and young to realize that Boo Radley is the person leaving them gifts in the tree but notices that her brother has a hunch about the person's identity. Scout even mentions,

He [Jem] had been on the verge of telling me something all evening; his face would brighten and he would lean toward me, then he would change his mind. (Lee, 63)

After they write a letter thanking the gift-giver, Jem attempts to leave their note in the knothole of the Radley tree and discovers that Nathan had filled the knothole with cement. When Jem asks Nathan why he filled the tree with cement, Nathan lies to him and tells Jem that he filled the knothole with cement because the tree is dying. After speaking to Atticus about Nathan's reason for filling the knothole with cement, Atticus confirms that the tree looks healthy, and Jem realizes that Nathan told him a lie.

It is implied that Jem understands Nathan's true intentions for filling the knothole with cement. Jem knows that Nathan wants to prevent his brother, Boo Radley, from communicating with them. Jem is also aware that his chances of developing a friendship with Boo Radley are over, which is why he cries by himself on the front porch.

Jem recognizes, as most readers probably do, that Nathan Radley cements the secret knothole of the oak tree to prevent further contact between his brother, Boo, and the Finch children. When Jem asks Boo's brother, Nathan tells him that the

"Tree's dyin'. You plug 'em with cement when they're sick. You ought to know that, Jem.

It is Nathan's way of symbolically treating the sickness that he believes still affects Boo. Somehow, Nathan must have witnessed Boo placing items in the tree late at night; or possibly, he saw Jem and Scout retrieving the items. Nathan may have even questioned Boo about it. In any case, he closed the opening, preventing Boo's only form of contact outside the Radley House. Although Jem figures it was out of pure meanness, Nathan probably thinks that Boo's contact with children might be considered improper, so he took the action he did. Jem isn't sure about the reason until Atticus points out that the tree is healthy.

"Look at the leaves, they're all green and full, no brown patches anywhere--... The tree's as healthy as you are, Jem."

It becomes obvious that Jem has been doing much thinking since the incident when he lost his pants on the Radleys' fence. At the time he told Scout,

“When I went back, they were folded across the fence… like they were expectin’ me.”

“And something else—” Jem’s voice was flat. “Show you when we get home. They’d been sewed up. Not like a lady sewed ‘em, like somethin’ I’d try to do. All crooked. It’s almost like—”

“—somebody knew you were comin‘ back for ’em.”

It is from this moment that Jem probably started thinking differently about Boo Radley and the supposed danger that he presented. He constantly speaks to Scout about the gifts they find in the knothole, trying to ascertain what her sentiments are. His reaction to her suggestions shows that he doubts that she would, or could, understand what was happening. It is evident that Jem, at this point, suspects that Boo Radley is the one placing the gifts in the knothole. He realizes, though, that it is beyond Scout to come to the same conclusion.

It is clear that Jem is developing feelings of compassion for Boo Radley. He is starting to realize that Boo is reaching out to them and his attempts at contact are symbolized by the objects he places in the knothole. It is obvious that the items they find took effort to make, were of sentimental value or were precious to the donor--this is what Jem realizes. To Scout, though, they are mere trinkets for their pleasure. This much is evident during their earlier conversations. When they first discover something in the knothole, Scout says: 

“Don’t take it, Jem,” I said. “This is somebody’s hidin‘ place.”

and he replies:

“I don’t think so, Scout.”

Jem also later states:

"You know it’s only when school’s in that we’ve found things.”

It is obvious that Jem, even at this early stage, suspects something more and, based on his earlier experience with the pants, might already have been thinking about Boo Radley as their generous donor.

The fact that Jem is so emotional about the knothole being closed symbolizes his growing sensitivity and awareness about what happens around him. He is starting to lose the obsessive focus that young children have with themselves and their immediate surroundings, so aptly illustrated by Scout. Younger children's awareness is informed by their selfish needs and wants, and it is difficult for them to extend that to others. Scout has clearly displayed her immaturity in this regard through her various altercations with other children such as, for example, Walter Cunningham.

Jem is heartbroken that Mr. Radley could be so cruel to deny Boo even one opportunity of contact with the world outside. Jem is sensible enough to realize that Boo has become a prisoner of his community's prejudice and of his own family's insensitive attitude. Ironically, just like Scout, the Radleys seem to have only been considering themselves and their interests, without giving Boo any regard or any chance of redemption at all.

Jem is overwhelmed by his realization and Scout tells us that he stayed outside on the porch for a long time: 

He stood there until nightfall, and I waited for him. When we went in the house I saw he had been crying; his face was dirty in the right places, but I thought it odd that I had not heard him.

Jem's sorrow was expressed in heartfelt and quiet weeping, just as an adult would grieve.